ancient india's contribution to mathematics

“India was the motherland of our race and Sanskrit the mother of Europe’s languages. India was the mother of our philosophy, of much of our mathematics, of the ideals embodied in Christianity... of self-government and democracy. In many ways, Mother India is the mother of us all.”- Will Durant (American Historian 1885-1981) Mathematics represents a high level of abstraction attained by the human mind. In India, Mathematics has its roots in Vedic literature which is nearly 4000 years old. Between 1000 B.C. and 1000 A.D. various treatises on Mathematics were authored by Indian mathematicians in which were set forth for the first time, the concept of zero, the techniques of Algebra and algorithm, square root and cube root. This method of graduated calculation was documented in the Pancha-Siddhantika (Five Principles) in the 5th Century. But the technique is said to be dating from Vedic times circa 2000 B.C. As in the applied sciences like production technology, architecture and shipbuilding, Indians in ancient times also made advances in abstract sciences like Mathematics and Astronomy. It has now been generally accepted that the technique of Algebra and the concept of zero was originated in India. But it would be surprising for us to know that even the rudiments of Geometry, called Rekha-Ganita in ancient India, were formulated and applied in the drafting of Mandalas for architectural purposes. They were also displayed in the geometric patterns used in many temple motifs. Many motifs in Hindu temples and Palaces display a mix of floral and geometric patterns. Even the technique of calculation, called algorithm, which is today widely used in designing software programs (instructions) for computers was also derived from Indian Mathematics. In this chapter we shall examine the advances made by Indian mathematicians in ancient times.

Algebra-The Other Mathematics In India around the 5th century A.D. a system of Mathematics that made astronomical calculations easy was developed. In those times its application was limited to Astronomy as its pioneers were astronomers. As astronomical calculations are complex and involve many variables that go into the derivation of unknown quantities. Algebra is a short-hand method of calculation and by this feature it scores over conventional Arithmetic. In ancient India conventional Mathematics termed Ganitam was known before the development of Algebra. This is borne out by the name - Bijaganitam, which was given to the algebraic form of computation. Bijaganitam means ‘the other Mathematics’ (Bija means ‘another’ or ‘second’ and Ganitam means Mathematics). The fact that this name was chosen for this system of computation implies that it was recognized as a parallel system of computation, different from the conventional one which was used since the past and was till then the only one. Some have interpreted the term Bija to mean seed, symbolizing origin or beginning. And the inference that Bijaganitam was the original form of computation is derived. Credence is lent to this view by the existence of Mathematics in the Vedic literature which was also shorthand method of computation. But whatever the origin of Algebra, it is certain that this technique of computation originated in India and was current around 1500 years back. Aryabhatta an Indian mathematican who lived in the 5th century A.D. has referred to Bijaganitam in his treatise on Mathematics, Aryabhattiya. An Indian mathematician - astronomer, Bhaskaracharya has also authored a treatise on this subject. the treatise which is dated around the 12th century A.D. is entitled ‘Siddhanta-Shiromani’ of which one section is entitled Bijaganitam. Thus the technique of algebraic computation was known and was developed in India in earlier times. From the 13th century onwards, India was subject to invasions from the Arabs and other Islamised communities like the Turks

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and Afghans. Alongwith these invader: came chroniclers and critics like Al-beruni who studied Indian society and polity. The Indian system of Mathematics could not have escaped their attention. It was also the age of the Islamic Renaissance and the Arabs generally improved upon the arts and sciences that they imbibed from the land they overran during their great Jehad. The system of Mathematics they observed in India was adapted by them and given the name ‘Al-Jabr’ meaning ‘the reunion of broken parts’. ‘Al’ means ‘The’ & ‘Jabr’ means ‘Reunion’. This name given by the Arabs indicates that they took it from an external source and amalgamated it with their concepts about Mathematics. Between the 10th to 13th centuries, the Christian kingdoms of Europe made numerous attempts to reconquer the birthplace of Jesus Christ from its Mohammedan-Arab rulers. These attempts called the Crusades failed in their military objective, but the contacts they created between oriental and occidental nations resulted in a massive exchange of ideas. The technique of Al-jabr could have passed on to the west at that time. During the renaissance in Europe, followed by the industrial revolution, the knowledge received from the east was further developed. Algebra as we know it today has lost any characteristics that betray it eastern origin save the fact that the term ‘Algebra’ is a corruption of the term ‘Al-jabr’ which the Arabs gave to Bijaganitam. Incidentally the term Bijaganit is still use in India to refer to this subject. In the year 1816, an Englishman by the name James Taylor translated Bhaskara’s Leelavati into English. A second English translation appeared in the following year (1817) by the English astronomer Henry Thomas Colebruke. Thus the works of this Indian mathematician astronomer were made known to the western world nearly 700 years after he had penned them, although his ideas had already reached the west through the Arabs many centuries earlier. In the words of the Australian Indologist A.L. Basham “The Wonder That Was India” the world owes most to India in the realm of Mathematics, which was developed in the Gupta period to a stage more advanced than that reached by any other nation of antiquity. The success of Indian Mathematics was mainly due to the fact that Indians had a clear conception of the abstract number as distinct from the numerical quantity of objects or spatial extension.” Thus Indians could take their mathematical concepts to an abstract plane and with the aid of a simple numerical notation devise a rudimentary Algebra as against the Greeks or the ancient Egyptians who due to their concern with the immediate measurement of physical objects remained confined to Mensuration and Geometry.

Geometry and Algorithm But even in the area of Geometry, Indian mathematicians had their contribution. There was an area of mathematical applications called Rekha Ganita (Line Computation). The Sulva Sutras, which literally mean ‘Rule of the Chord’ give geometrical methods of constructing altars and temples. The temples layouts were called Mandalas. Some of important works in this field are by Apastamba, Baudhayana, Hiranyakesin, Manava, Varaha and Vadhula. The Buddhist Pagodas borrowed their plan of construction from the geometric grid of the Mandala used for constructing temples in India. (A majestic Pagoda at Bangkok) The Arab scholar Mohammed IBN Jubair Al Battani studied Indian use of ratios from Rekha Ganita and introduced them among the Arab scholars like AL Khwarazmi, Washiya and ABE Mashar who incorporated the newly acquired knowledge of Algebra and other branches of Indian Mathematics into the Arab ideas about the subject. The chief exponent of this Indo-Arab amalgam in Mathematics was Al Khwarazmi who evolved a technique of calculation from Indian sources. This technique which was named by westerners after Al Khwarazmi as “Algorismi” gave us the modern term Algorithm, which is used in computer software.

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Algorithm which is a process of calculation based on decimal notation numbers. This method was deduced by Al Khwarazmi from the Indian techniques geometric computation which he had studieds. Al Khwarazmi’s work was translated into Latin under the title “De Numero Indico” which means ‘of Indian Numerals’ thus betraying its Indian origin. This translation which belong to the 12th century A.D credited to one Adelard who lived in a town called Bath in Britian. Thus AL Khwarazmi and Adelard could looked upon as pioneers who transmited Indian numerals to the west. Incidents according to the Oxford Dictionary, word algorithm which we use in the English language is a corruption of the name Khwarazmi which literally means ‘a person from Khawarizm’, which was the name of the town where AL Khwarazmi lived. Today unfortunately, the original Indian texts that AL Khwarazmi studied are lost to us, only the translations are available. The Arabs borrowed so much from India in the field of Mathematics that even the subject of Mathematics in Arabic came to known as Hindsa which means ‘from India and a mathematician or engineer in Arabic is called Muhandis which means ‘an expert in Mathematics’. The word Muhandis possibly derived from the Arabic term Mathematics viz. Hindsa.

The Concept of Zero The concept of zero also originated in ancient India. This concept may seem to be a very ordinary one and a claim to its discovery may be viewed as queer. But if one gives a hard thought to this concept it would be seen that zero is not just a numeral. Apart from being a numeral, it is also a concept, and a fundamental one at that. It is fundamental because, terms to identify visible or perceptible objects do not require much ingenuity. But a concept and symbol that connotes nullity represents a qualitative advancement of the human capacity of abstraction. In absence of a concept of zero there could have been only positive numerals in computation, the inclusion of zero in Mathematics opened up a new dimension of negative numerals and gave a cut off point and a standard in the measurability of qualities whose extremes are as yet unknown to human beings, such as temperature. In ancient India this numeral was used in computation, it was indicated by a dot and was termed Pujyam. Even today we use this term for zero along with the more current term Shunyam meaning a blank. But queerly the term Pujyam also means holy. Param-Pujya is a prefix used in written communication with elders. In this case it means respected or esteemed. The reason why the term Pujya - meaning blank - came to be sanctified can only be guessed. Indian philosophy has glorified concepts like the material world being an illusion (Maya), the act of renouncing the material world (Tyaga) and the goal of merging into the void of eternity (Nirvana). Herein could lie the reason how the mathematical concept of zero got a philosophical connotation of reverence. In a queer way the concept of ‘Zero’ or Shunya is derived from the concept of a void. The The concept of void existed in Hindu Philosophy hence the derivation of a symbol for it. The concept of Shunyata, influenced South-East Asian culture through the Buddhist concept of Nirvana ‘attaining salvation by merging into the void of eternity’ (Ornate Entrance of a Buddhist temple in Laos) It is possible that like the technique of Algebra; the concept of zero also reached the west through the Arabs. In ancient India the terms used to describe zero included Pujyam, Shunyam, Bindu the concept of a void or blank was termed as Shukla and Shubra. The Arabs refer to the zero as Siphra or Sifr from which we have the English terms Cipher or Cypher. In English the term Cipher connotes zero or any Arabic numeral. Thus it is evident that the term Cipher is derived from the Arabic Sifr which in turn is quite close to the Sanskrit term Shubra.

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The ancient India astronomer Brahmagupta is credited with having put forth the concept of zero for the first time: Brahmagupta is said to have been born the year 598 A.D. at Bhillamala (today’s Bhinmal ) in Gujarat, Western India. Not much is known about Brahmagupta’s early life. We are told that his name as a mathematician was well established when K Vyaghramukha of the Chapa dyansty made him the court astronomer. Of his two treatises, Brahma-sputa siddhanta and Karanakhandakhadyaka, first is more famous. It was a corrected version of the old astronomical text, Brahma siddhanta. It was in his Brahma-sputa siddhanta, for the first time ever had been formulated the rules of the operation zero, foreshadowing the decimal system numeration. With the integration of zero into the numerals it became possible to note higher numerals with limited characters. In the earlier Roman and Babylonian systems of numeration, a large number of characters were required to denote higher numerals. Thus enumeration and computation became unwieldy. For instance, as in the Roman system of numeration, the number thirty would have to be written as XXX, while as per the decimal system it would 30, further the number thirty three would be XXXIII as per the Roman system, would be 33 as per the decimal system. Thus it is clear how the introduction of the decimal system made possible the writing of numerals having a high value with limited characters. This also made computation easier. Apart from developing the decimal system based on the incorporation of zero in enumeration, Brahmagupta also arrived at solutions for indeterminate equations of the type ax2+1=y2 and thus can be called the founder of higher branch of mathematics called numerical analysis. Brahmagupta’s treatise Brahma-sputa-siddhanta was translated into Arabic under the title ‘Sind Hind’. For several centuries this translation maintained a standard text of reference in the Arab world. It was from this translation of an Indian text on Mathematics that the Arab mathematicians perfected the decimal system and gave the world its current system of enumeration which we call the Arab numerals, which are originally Indian numerals.

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HYDRODYNAMIC ANALOGY TO QUANTUM MECHANICS G.C. Shukla

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MEDICAL LASER SYSTEMS AND THEIR APPLICATIONS Jagpal Singh

Introduction The art and science of surgery have evolved remarkably over the past centuries. While the knife traditionally has been regarded as the basic surgical tool, the advent of sophisticated medical devices has extended the armamentarium and precision of surgical techniques. The newest surgical devices utilized by surgeon are lasers. Lasers use extremely high energy light waves in order to cut through tissue in a very accurate manner, and to coagulate and remove tissue. Lasers have produced dramatic surgical effect that have improved the quality of care for patients. Hardly any laser application fascinates people more than medical applications. They expect laser to heel them with in no time. Lasers are used for many surgical application. For example laser are employed to prevent visual loss in patients with diabetes, to reduce intra ocular pressure in patients with glaucoma, to remove cancerous lesions inside the body, to cut away plaques in the blood vessels of the heart, and to treat skin cancer. The world market for laser sources used in medical applications alone is estimated to have reached $ 670 million in 2003, and large percentage of this volume is driven by cosmetic application such as the removal of hair, wrinkles, tattoos and skin spots. In some cases, correction defective vision is also considered a cosmetic application. But removing tissue to normalize the refractive power of the eye is one of the most rapidly growing medical applications. There are many medical laser system available today, but they all use the principle of selective photothermolysis, which means getting the right amount of the right wavelength of laser energy to the right tissue to damage or destroy only that tissue, and nothing else. As with any surgical procedure, the key to a successful outcome is a knowledgeable, experienced and skillful surgeon. The surgeon who uses lasers should understand the technology being employed, be well trained in its use and be capable of managing potential complications and meet the high standards of his or her medical peers. Therefore, following parameters should be kept in mind before selecting any laser for particular application.

Laser Parameters: The Right Wavelength Most medical laser devices deliver only one wavelength of laser light, and the laser surgeon must choose the right wavelength for the specific tissue involved. Some lasers can be “frequency doubled”, and can be deliver two wavelength of laser light, and a very few are tunable over a narrow range of wavelength. Some lasers can be used in different modes, for example, Q-Switched and long pulse. The Right Amount of Laser Energy Almost all medical laser surgeon to adjust the power setting and duration of the laser pulse. As a general rule, the length of the laser pulse is as important as the wavelength or the power setting in determining its medical use. Lasers can operated in continuous wave (CW) or pulsed mode. CW lasers emit a steady beam for as long as the laser medium is excited. If this steady beam is held on tissue longer than the thermal relaxation time, excessive heat will be conducted into normal tissue, which may delay healing and increasing scarring. All CW lasers may be pulsed , either mechanically using a shutter, or by electronic means. Pulsed lasers emit light in individual pulses, which may be long pulsed (thousandths of second) or short pulse (millionths of a second) Q Switching allows the laser to store energy between pulses, enabling very high power output.

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Right Laser Beam Delivery Device for Target Tissue The laser surgeon uses a delivery device to get the laser energy to the tissue. These devices include special fiber optic cable with hand pieces, or articulated arms, in which specially reflecting mirrors are mounted in tubes, which rotate about the axis of the mirrors, The laser light is reflected from mirror to mirror through the tube out to the patient. Special devices may be attached to the hand pieces of either fiber optic cables or articulated arms, including slit lamps for use on the eye, operating microscope for use in the ear and throat, insulated fibers for use with endoscopes in gastrointestinal and bronchial surgery, and Scanners, which scan the laser beam in a preset pattern and limit the time a CW laser beam dwells on the target tissue. Certain lasers are only used for very specific conditions. Medical lasers are not magic-they are only tools, and one should always select the right tool for the right job. Some of the medical lasers currently used with their applications are given below:

Types of Lasers and their Applications Ruby Laser: The Ruby Laser emits red light with a wavelength of 694 nm. The lasing medium is a synthetic ruby crystal of aluminum oxide and chromium atoms, which is exited by flash lamps. The first laser system to be built by T.H. Maiman in 1960, early ruby laser systems were used for retinal surgery, but were not suitable for dermatological work until the development of Q-Switching technology in the mid 1980’s. Ruby laser light is strongly absorbed by blue and black pigment, and by melanin in skin and hair. Modern ruby laser systems are available in Q-Switched mode with an articulating arm, “free running” (millisecond range) mode with a fiber optic cable delivery, or as dual mode lasers. Current uses include: Treatment of tattoos (Q-Switched mode), Treatment of pigmented lesions including freckles, liver spots, Nevus of Ota, café-au-lait spots (Q-Switched mode) Laser hair Removal (free-running mode) Alexandrite Laser: Similar to the ruby laser, the Alexandrite Laser contains a rod of synthetic chrysoberyl, a gemstone discovered in Russia in 1830 on Czar Alexander II’s 13th birthday. It emits a deep red light at 755 nm, and has properties similar to the ruby laser. It’s slightly longer wavelength permits slightly deeper penetration into skin, with slightly less absorption by melanin. Principal uses include laser hair removal in millisecond-range pulsed mode, and tattoo removal in Q-Switched mode. YAG Lasers: Lasers use an Yttrium-Aluminum-Garnet (YAG) crystal rod as the lasing medium. Dispersed in the YAG rod are atoms of rare earth elements, such as neodymium (Nd), Erbium (Er) or Holmium (Ho), which are responsible for the different properties of each laser. All YAG lasers may be operated in continuous, / or pulsed, or Q-switched mode. Continuous and pulsed delivery is through fiber optic cables, either bare-fiber or through hand piece or scanners, and Q-switched delivery, because of the very high power, is through an articulated arm. Nd: YAG Laser: A true workhorse, the Nd: YAG emits a near-infrared invisible light at 1064 nm it may be delivered in CW mode through a fiber to a sapphire tip to cut tissue, or because of its deep penetration, used to directly coagulate tissue. The Q-Switched Nd:YAG is effective for black tattoo ink, and has been used with fair results for hair removal. Millisecond-range Nd:YAG laser light is very effective for long-term hair removal. Er: YAG Laser: Often referred to as the “Erbium” laser, emits a mid-infrared beam at 2940 nm, which coincides with the absorption peak for water. Its principal use is to ablate tissue for cosmetic laser resurfacing for wrinkles. The Erbium laser has been advertised to offer advantages of reduced redness, decreased side effects and rapid healing compared to the pulsed or scanned CO2 laser, but does so by its limited penetration into tissue, which limits the results compared to the more versatile CO2 laser. It has also been used as a dental drill substitute to prepare cavities for filling. Ho: YAG Laser: Relatively new to the medical/dental fields, the Ho: YAG laser emits a mid infrared beam at 2070 nm. It’s principal use is to precisely ablate bone and cartilage, with many application in orthopedics for

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arthroscopy, urology for lithotripsy (removal of kidney stones), ENT for endoscopic sinus surgery, and spine surgery for endoscopic disc removal. The Ho: YAG laser was recently approved for TURP (prostate removal) KTP Laser: When Nd:YAG laser light at 1064 nm is passed through a potassium-titanyl-phosphate (KTP) crystal, the wavelength is halved to 532 nm, a brilliant green light used in CW mode to cut tissue, in pulse mode for vascular lesion including facial and leg veins, fiber hand piece, scanner, or microscope for CW/pulse mode, and articulating arm for Q-Switched mode. Diode Lasers: Diode lasers are solid-state device similar in construction to LED’s. The familiar “laser pointers” are in fact diode lasers. Diode lasers used clinically emit near-infrared light in the 800-900 nm range. Currently their principal application is in millisecond-range pulsed mode for laser hair removal, and for periodontal surgery. Other applications include treatment of leg and facial veins. Diode bars are also used to exite or “pump” more traditional laser media, for example YAG rods. Because of their relative simplicity and low maintenance requirements, Diode lasers and Diode-pumped solid-state lasers will be used more in the near future as more wavelengths become available. Copper Vapor Laser: Vaporized copper bromide is the lasing medium in the copper vapor Laser (CVL), which emits yellow light at 577 nm and green light at 511 nm, delivered through a fiber optic cable. Unlike the PDL, there is no purpura because of the longer pulse duration. However, a long warm up time and short laser cavity life make the CVL a less popular choice than the PDL for vascular lesions. Excimer Laser: Noble gas Halide, or Excimer lasers, emits UV invisible light that triggers a photochemical reaction on the target tissue. This very short wavelength is capable of high resolution and microscopic surgery. The most common medical application is the Argon-Fluorine (Ar: F) laser at 193 nm, used for PRK and LASIK (Laser in situ Keratomilieusis) vision correction. The laser beam is delivered through an operating microscope integrated with the laser housing and operating table. Excimer laser radiation shows great promise for cardiac revisualization and lithotripsy, but is currently limited by the lack of durable-UV capable fiber optic delivery devices. Argon Laser: One of the first lasers to be used clinically, the Argon (or argon-ion) laser is a continuous wave (CW) gas laser that emits blue-green light at 488 and 514 nm. Argon laser light is strongly absorbed by hemoglobin and melanin. Although the beam may be mechanically pulsed, there’s significant non-selective heating in surrounding tissues, thus increasing the chance of scare formation. Delivery is through a fiber optic cable, slit lamp, or operating microscope. Uses include: Retinal and inner ear surgery; Treatment of thick or nodular port wine birthmarks; Facial spider veins; Small dark moles (junctional nevi);Cherry hemangioma. CO2 Laser: Often referred to as the “surgical laser”, the action of the co2 laser most resembles traditional surgery. Unlike any other medical laser, its action on tissue is directly visible as it used. The CO2 laser was the first laser widely used by surgeons, and is still the most used of all the medical lasers. The CO2 laser emits continuous wave (CW) or pulsed far infrared light at 10,600 nanometers (nm), which can be focused into thin beam and used to cut like a scalpel, or defocused to vaporize, ablate, or shave soft tissue. Strongly absorbed by water, which constitutes over 80% of soft tissue The CO2 laser may be operated in pulsed mode or used with scanning devices to precisely control the depth and area of ablation. The CO2 Laser are mainly used for; Removal of benign skin lesion, such as moles, warts, keratoses, as a “laser scalpel” in patients or body areas prone to bleeding, “No-Touch” removal of tumors, especially of the brain and spinal cord, Laser surgery for snoring, Shaving, dermabrading, and resurfacing scars, rhinophyma, skin irregularities. Cosmetic Laser Resurfacing for wrinkles, etc Nitrogen Laser: Nitrogen laser emits light in UV range at 337 nm. Two types of nitrogen lasers have been developed for bio medical applications. The first laser system, developed for treatment of pulmonary tuberculosis, delivers an average power of 2.5-milli watt at a repetition rate of 100 pps, each pulse of 7ns (FWHM) duration. The laser beam is delivered through an optical fiber with core diameter of 400 microns and numerical apertures of ~0.2 Laser on/off control is achieved with the help of an electronic timer, if required. A series resonant switched mode power supply of 15 KV, 200W rating has been developed for this laser, which reduces both the weight and the volume of the system considerably. The supply operates at 50 KHz to charge the storage capacitors. This laser is

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being used for treatment of pulmonary tuberculosis. The laser beam is introduced into the cavity with the help of the optical fiber mentioned above. The second type of nitrogen laser developed operates at 20pps with a peak power of ~150 KW and pulse duration of 7 nanoseconds. This system uses a thyratron as a high-speed switch. A switched mode power supply similar to the one mentioned above is used for this laser with a provision to vary the repetition rate and the laser power. This system are used mainly for studying the effect of the UV laser radiation on microbial suspensions containing photosensitive dyes and on microorganisms, immunoglobulin levels, phagocytes, macrophage activity and such other areas.

Pulsed Dye Laser Because the yellow light at 577-585 nm coincides with the peak absorption of heamoglobin in blood, the pulsed dye laser (PDL) is useful to treat vascular lesions. A lasing medium of Rhoda mine dye is excited by flash lamps, emitting a pulse in the range of 450 microseconds in (1500 microseconds in some of the newer PDL’s), just less than the thermal relaxation time of minute blood vessels. Originally developed in the late 1980’s Pulsed dye Laser became the preferred laser for the treatment of vascular lesions, including spider veins, strawberry birthmarks and port wine stains, replacing the argon laser because of the PDL’s decreased heat damage and decreased chance of scarring. However, the PDL’s short pulse and high absorption rupture the targeted blood vessels, causing unsightly purpura (black and blue marks), which can last up to 2 weeks. Currently, less expensive, more reliable green light lasers such as the KTP and other Frequency doubled Nd: YAG is used for most vascular lesions. The pulsed dye laser remains the treatment of choice for: Port wine stains, especially in infants and children’s, Laser treatment of thick red scares. Summary: Laser surgery provides an alternative to older more invasive surgical techniques, resulting in more rapid healing and a reduction of complications. However, laser surgery is neither simple nor without associated serious risks, including edema, elevation of interlobular pressure, penetration of a blood vessel with bleeding, tissue necrosis etc. Therefore, the optimal use of lasers demands much more than just technical expertise; a comprehensive knowledge and experience related to pathological disease processes and their treatment is also required. Laser has proved to be safe and effective instruments in ophthalmology, when used by surgeons possessing a broad base of knowledge, training and clinical experience. Continued success in existing and new laser surgical application will depend on many interrelated aspects of the physician’s expertise and judgment: a comprehensive eye examination and proper medical diagnosis; a weighing of risks, benefits, and available recourse to alternative surgical and medical treatments; precise timing and selection of the laser technique to fit the individual patient’s circumstances; a technical proficiency in controlling and manipulating lasers; a familiarity with associated adverse events and a readness to response as warranted, and a personal responsibility for the post operative management of patients undergoing laser surgery.

Introduction Problems involving counting are very common in Discrete Mathematics. The formal study of counting problems is called Combinatorics or Combinatorial Analysis. There are many complicated combinatorial techniques used by mathematicians to solve complex counting problems. However most of them are based on a few basic principles of counting which will be discussed in the following section.

Rules of Counting The following simple rule is the grandfather of all counting rules. Multiplication Rule If there are m ways of making a choice and n ways of making another choice then there are mn ways of making both choices. Note: This rule can be extended for any finite number of choices. Examples a) Multiple Classifications.Suppose that people are classified according to sex,marital status and profession. Then if there are 15 professions we will have 15x2x2 = 60 classes in all. b) Placing r indistinguishable balls in n cells. Each of the r balls has n choices of cells. Thus there are nr ways in all. The following rule is for those combinatorial problems in which order matters such as the arrangement of three letters P,O,T may produce the words TOP and POT which are both different and the order matters here. Ordered Samples There are two types of ordered samples with and without repetition. Ordered Samples with repetition If repetitions are allowed then the number of ordered samples of size k for an n element set is nk. Examples a) Word Arrangements: The possible number of 10 letter words are 2610 as the letters can be selected from the 26 letters of the English Alphabet. b) Coin Tossing: Tossing a coin r times is equivalent to drawing ordered samples of size r from a set {H,T} The total number of ways is then 2r. Ordered Samples without repetition If repetitions are not allowed then the number of ordered samples of size k for an n element set are n.n-1…n-k+1. Note: The number of ordered samples of size n from an n element set without repetitions ofcourse is n!. Examples a) Birthdays: The (different or not repetitive) birthdays of r people form an ordered sample of size r without repetition from a 365 days set and thus the number of such birthdays is 365.365-1…365-r+1.

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b) Placing n indistinguishable balls in n cells(without repetition). The number of ways of placing n balls in n cells (one ball in each cell and without repeating any ball in any cell) is n.n-1…1 = n!. Unordered Samples without repetition If repetitions are not allowed then the number of unordered samples of size k from an n element set are (n.n-1…nk+1)/k! Note: This is same as placing n different balls in k cells so that no cell is empty. Examples a) Subsets: Thenumber of 3 element subsets from a 4 element set are 4.3.2/3! = 4. b) Teams: The number of 5 member teams formed from groups A,B and C of 6,7 and 8 people respectively will be (21.20….21-5+1)/5! c) Urns: An urn contains 5 white and 3 red balls.The number of ways in which 3 white and 2 red balls can be drawn are (5.4.5-3+1)(3.3-2+1)/3!2! Unordered Samples with repetition If repetition is allowed then the number of unordered samples of size k from an n element set are (n.n+1…n+k-1)/k! Examples a) Placing r indistinguishable balls in n cells(without any restriction that no cell is empty). The number of ways of placing r similar balls in n cells can be given as (n.n+1…n+r-1)/r! b) Possible no of solutions of an equation. The number of different solutions of the equation r1+r2+…rn= r are (n.n+1…n+r-1)/r! Permtations involving indistinguishable object Thenumber of different arrangements of n different objects of which k1 objects are indistinguishable and are of onetype, k2 objects are indistinguishable and are of another type and so on km objects are indistingui-shable and are of another type are n!/(n1! n2!…n3!) Examples a) Coin Tossing: The no of ways of getting 13 headsand 7 tails in 20 tosses of a coin are 20!/13!7! b) Flags: The number of ways of displaying 3 red and 4 blue flags are 7!/(3!4!). Principle of Inclusion and Exclusion The principle of inclusion and exclusion for three arbitrary sets A,B and C is n(A UBUC) = n(A)+n(B)+n(C)-n(A

B)-n(A

C) –n(B

C)+n(A

B

C)

Note: The above can be extended for any arbitrary number of sets. Example In a group of 100 people in a room 60 are men, 30 are young and 10 are young men. How many are old women? The answer follows easily from a reduced form of the above principle for 2 sets viz.20 old women.

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SIXTEEN SUTRAS OF VEDIC MATHEMATICS Kalika Srivastava

The present article is an attempt to give some examples on the applications of first four sutras out of sixteen sutras of Vedic Mathematics. ‘Vedic Mathematics’ is the name given to the ancient system of Mathematics. As the basic principles of Hinduism lie in the Vedas, roots of Mathematics also. Thousand of years ago, Vedic Mathematicians authored various dissertations and now it is widely accepted that these treatises laid down the foundations of algebra, algorithm, square roots, cube roots, varios methods of calculations and the concept of zero. The sixteen sutras are 1. Ekadhikena Purvena 2. Nikhilam Navatashcaramam Dashatah 3. Urdhva - Tiryabhyam 4. Paraavartya Yojayet 5. Shunyam Saamyasamuccaye 6. (Anurupya) Shunyamanyat 7. Sankalna - Vyavalalanabhyam 8. Puranapuranabhyam 9. Chalana - Kalanabhyam 10. Yaavadunam 11. Vyashtisamanshtih 12. Shesanyankena Charamena 13. Sopaanty advayamantyam 14. Ekanynena Purvena 15. Gunitasamuchyah 16. Gunakasamuchyah

Thus papa is 11, mara is 52. Words kappa, tapa, papa and yapa all mean the same, that is 11.

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1. Ekadhikena Purvena Meaning: ‘By one more than the previous one’ This sutra is used for either multiplication or division because of the key word ‘by’. Applications of the sutra (i) Squares of numbers ending in 5. Example 252. The last number is 5 and the previous digit is 2. One more than the previous digit is 3. This sutra tells us to multiply the previous digit 2 by one more than itself. That is 3x2=6 and the latter one is multiplied by itself, i.e. 52 = 25. Therefore 252 = 3x2 / 52 =625. Here / represents the separation of first and the latter part. Similarly 1052 = 11x10 / 25 =11025 The above sutra is valid for both two and three digit numbers. (ii) Fractions whose denominators are numbers ending in nine. There are two methods of finding these fractions. Division method and multiplication method. Division Method 1/19: The number of decimal places before repetition is the difference numerator and the denominator i.e. 18 places. For the number nineteen , purva is 1 and ekadhikena purva is 1+1=2. The following steps are applied Step I Step II Step III Step IV Step V Step VI Step VII

Repeating these steps 18 times, we get the answer as .052631578947368421 Multiplication Method As above, the purva is 1 and Ekadhikena purva is 1+1=2. The multiplication method in which 2 is the multiplier, is explained as Step I Step II Step III Step IV Step V Step VI Step VII

Repeating as above, we get the answer, in which the digits in the answer are written in the backward direction. A very important observation in the above example is made as Sum of first and the tenth digit = 1+8 =9

16

Sum of second and the eleventh digit

=9

Sum of third and the twelfth digit

=9

And so on. Therefore in the division process, we need to find only first 9 digits, remaining digits can be found by taking their complements and in the multiplication method, vice-versa.

2. ‘Nikhilam Navatas’ Caramam Dasatah Meaning: ‘All from 9 and the last from 10’. This formula can be applied in multiplication of numbers which are nearer to bases like 10, 100, 1000 etc. The numbers taken can be either less or more than the base considered. The difference between the number and the base is called deviation which can be positive or negative. The negative deviation is written using a bar on the number. Example: 993-1000 = 007 Some rules of the method (in which both the numbers are near to the base) (i) The number 94. All from 9 and the last from 10 means. 9-9 = 0 and 10 - 4 =6, gives us 06. (ii) The numbers are written one below other and the deviations are written on their right side. 8

2

7

3

(iii) The right side of the product is the product of the deviations, which will contain the number of digits as no. of zeros in the base. Therefore 3x2=6. (iv) The left side of the product is the sum of one number with the deviation of the other. In the above example, 8 3=6, or 7-2=5. Hence the number is 56. (v) If R.H.S. contains less number of digits than the number of zeros in the base, then the remaining digits are filled up by writing zeros on the left side of the R.H.S. and if it has excess digits, they are added to L.H.S. of the answer. Illustration of above rules is given as: Case i. When the numbers are lower than the base (a) With base 10 Example: 7x8 is already discussed earlier. (b) With base 100 Example: 96x 95 96

4

95

5

91

/ 20 = 9120

(c) With base as 1000 Example: 983x 985 983

017

985

015

968 / 255 = 968255

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Application of rule (v) 755 x 995 755

245

995

005

750

/ 1225 = 751225

Case–II: Both the numbers are higher than the base. This is same as the previous case. Only difference lies in cross adding instead of substracting Examples: With base 10, 18x15 18 15 23

Case–III: One number is more and the other is less than the base. In this case one deviation is (+) and the other is (-). Hence the right hand side has to be substracted as shown in the examples below: (a) 12x8 12 08 10 /

2. Nikhilam in Division Case–I: When the dividend is a two digit number and the divisor is 9.

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Rule: The quotient is the first digit and the remainder is quotient + second digit. Example: 41÷ 9, Q = 4, R = 4+1 Case–II: When the number is three digits or four digits number etc. Rule: Add the first digit to the second digit no. and place the sum as the digit after the first digit to get the first part of the quotient. Then the second digit of this part is added to the third digit and the sum is placed after the first part of the quotient. Proceeding in this way, add the last digit of the quotient to the last digit of the quotient to get the remainder. Examples: (a) 610 9 : First digit 6, 6+1=7, so the first part of the quotient is 67. Now add 7 to the last digit 0 to get the remainder as 7. Thus Q = 56, R=7. (c) 121301÷ 9, 1+2 =3, first part of the quotient 13, 3+1=4, hence the quotient becomes 134, 4+3=7, Q becomes 1347, 7+0=7, Q=13477, Remainder is 7+1= 8. Hence the final answer is Q=13477, R=8. Case–III: When the remainder is equal to 9 or more than 9. We repeat the process to divide the remainder by 9. This quotient is added to the quotient obtained and the remainder is kept as the as the final remainder. For example, in the example (b) above, if the number is 12302 then the remainder is 9, 9 when divided by 9 gives 1as quotient and 0 as the remainder. Therefore, the final Q= 13478 and R = 0. also, if the number is 12305, then remainder is 7+5=12, 12 divided by 9, gives Q as 1 and remainder1+2=3. Therefore the final quotient is 13478 and remainder is 3.

3. Urdhva Tiryagbhyam This formula is applicable to all cases of multiplication and also division of a large number by another large number. Meaning: Vertically and crosswise. This can be explained with the proof of two digits, three digits and can be done for more digits numbers in a similar fashion. Observation: Any two digits and three digits no. can be written in the form ax + b and ax2 + bx + c, with x =10. Hence (i) ax +b X cx +d is an expression containing x2, x and constant. Obviously coeff. Of x2 is a x c, coeff. of x is ad + bc and the const. is b x d. This can be well explained with the help of arrowed figure shown below: a b c

2 x 6=12. Hence 2 is retained and 1 is carried over and kept below the second digit.

Step II

4 x 6 + 5 x 2 = 34, 4 is retained and 3 is carried over and kept below the third digit.

Step III

4 x 5=20

Hence 2042 + 31 2352 (b)

1

3

8

3

3

6

Step I

8 x 6 = 48, 8 is kept and 4 is carried over.

Step I

3 x 6 + 8 x 3 =42, 2 is retained and 4 is carried over.

Step III

1x6 + 8x3 + 3x3 = 39, 9 kept and 3 carried over

Step IV

1x3 + 3x3 = 12, 2 kept and 1 carry over

Step V

1x3

Hence, the answer is 32928 1344 4 6368 Note: The above method can be effectively used in multiplication of algebraic expression also. Urdhva in division process: This sutra is applied for division process, particularly in algebra as shown in the example below: Division of x3 + 5x2 + 3x + 7 by x-2 Step I- x3 divided by x gives x2. Hence x2 is the first term of the quotient. Step II- x2 x (-2)= -2x2, but in the dividend, the term is 5x2, which is 7x2 more than -2x2. This can be obtained by multiplying 7x with x . Therefore, the next term is 7x.

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Step III- 7x X -2 = -14x, which is 17x more than 3x. This can be obtained by keeping the next term as 17. Step IV- 17 X -2 = -34, which is 7+34 more than than the term , but there is no term left in the dividend. Hence 41 is the remainder. Answer is Q= x2 + 7x + 17, R = 41.

4. Paravartya Yojayet Meaning: Transpose and apply For explaining this sutra, we take different cases Divisors have more than one digit and are slightly greater than powers of ten. Example1: Divide 1225 by 12 The solution can be explained in the following steps Step I- Write the divisor leaving the first digit, write the other digit or digits using (-)ve sign and place them below the divisor as shown 12 -2 Step II- Write the dividend to the right and set apart the last one digit for the remainder (as no. of digits in the divisor is 2) 12 122 5 -2 Step III- Write the first digit below the horizontal line drawn under the dividend. Multiply the digit by -2, write the product below the second digit and add, i.e. 12 122 5 -2 -2 10 Step IV- Multiply 0 by -2 and place it below the 3rd digit and add. 12 122 5 -2 -20 102 Step V- Continue the process to the last digit i.e. 12 122 5 -2 -20 -4 102 1 Step VI- The sum of the last digit is the remainder and the result to its left is the quotient. Thus Q=102, R=1. Example of three digits divisor: Divide 2598 by 123 Since the divisor is of three digits, the last two digits of the dividend are set up for the remainder. The remaining steps with the series of multiplication with -2 and -3 are shown below 123 -2-3

25 -4

21 Q=21, R=15

9 -6

8

-2-3 15

21

Example 3: When the divisor has five digits. So the last four digits are to be set up for the remainder. Divide 239479 by 11213 Steps are shown below 11213

Other than the applications discussed above, these four methods have many more applications. It is said that originally there were 16 volumes (one on each sutra, authored by Jagadguru Sankracharya), but most of the literature got misplaced. Later on, many of Guruji’s disciples and other mathematicians researched on the above topic and consequently, lot of literature now is available for the people having interest in the subject.

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PHARMACOGENOMICS KNOW YOUR PERSONALIZED MEDICINE Jyoti Sinha

Introduction One Size Fit All - Traditional Approach in Medicine One of the major problems in medicine is that a medicine (commonly referred as drug in pharmaceutical science) will not function to the same degree of efficacy in all patients. Often drugs will only exert the desired therapeutic effect in perhaps 30-70 per cent of patients. Anti-depressants, for example, are notorious for being successful in only 30 per cent of cases; the other 70 per cent are described as non-responders. Furthermore, drugs may function as predicted in one population of patients whilst in others it may lead to an adverse drug reaction. The reason for this differential of action is due to a person’s specific genetic make up which allows for a difference in how a drug is metabolized. The new discipline of pharmacogenomics investigated this all too important interaction between a putative pharmacological agent(drug) and persons genes.. The underlying aim of pharmacogenomics would be to tailor a drug to a person’s genes, ushering in the era of personalized medicine. Currently, physicians prescribe medication through a trial-and-error method. If the prescribed medication does not work for the patient the first time, the physician will try a different drug or dosage, repeating the process until the patient improves. Today, doctors have to use trial and error to find the best drug to treat a particular patient as those with the same clinical symptoms can show a wide range of responses to the same treatment. In future, doctors will be able to analyze a patient’s genetic profile and prescribe the best available drug therapy and dosage from the beginning. Pharmacogenomics - One Size Does Not Fit All Pharmacogenomics is the study of how an individual’s genetic inheritance affects the body’s response to drugs. This term comes from the words pharmacology and genomic and is thus the intersection of pharmaceuticals and genetics meaning how the drugs in future will depend on the genetic make-up of an individual. Researchers in the field are working on applying human genome knowledge to pharmaceuticals by identifying genes that account for varying drug reactions in different people. Eventually, they hope to be able to customize drug therapies for specific patient populations or even individuals. Pharmacogenomics holds the promise that drugs might one day be tailor-made for individuals and adapted to each person’s own genetic makeup. Environment, diet, age, lifestyle, and state of health all can influence a person’s response to medicines, but understanding an individual’s genetic makeup is thought to be the key to creating personalized drugs with greater efficacy and safety.

Anticipated Benefits of Pharmacogenomics More Powerful Medicines Pharmaceutical companies will be able to create drugs based on the proteins, enzymes, and RNA molecules associated with genes and diseases. This will facilitate drug discovery and allow drug makers to produce a therapy more targeted to specific diseases. This accuracy not only will maximize therapeutic effects but also decrease damage to nearby healthy cells.

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Better, Safer Drugs the First Time Instead of the standard trial-and-error method of matching patients with the right drugs, doctors will be able to analyze a patient’s genetic profile and prescribe the best available drug therapy from the beginning. Not only will this take the guesswork out of finding the right drug, it will speed recovery time and increase safety as the likelihood of adverse reactions is eliminated. Dosages Current methods of depending dosages on weight and age will be replaced with dosages based on a person’s genetics – how well the body processes the medicine and the time it takes to metabolize it. This will maximize the therapy’s value and decrease the likelihood of overdose.

Advanced Screening for Disease Knowing one’s genetic code will allow a person to make adequate lifestyle and environmental changes at an early age so as to avoid or lessen the severity of a genetic disease. Likewise, advance knowledge of particular disease susceptibility will allow careful monitoring, and treatments can be introduced at the most appropriate stage to maximize their therapy. Decrease in the Overall Cost of Health Care Decreases in the number of adverse drug reactions, the number of failed drug trials, the time it takes to get a drug approved, the length of time patients are on medication, the number of medications patients must take to find an effective therapy, the effects of a disease on the body (through early detection), and an increase in the range of possible drug targets will promote a net decrease in the cost of health care

Pharmacogenomics is best possible with the help of BIOINFORMATICS Bioinformatics • A city with a telephone network needs a telephone directory. Similarly, scientists studying genes need software to organize genetic data. Information science has been applied to biology to produce the field called Bioinformatics. Bioinformatics uses software to study the location of genes on a chromosome and how the genes interact with each other. Bioinformatics is the use of IT in biotechnology for the data storage, data warehousing and analyzing the DNA sequences. DNA sequencing is the pattern of arrangement of genetic material. It is the comprehensive application of mathematics (e.g., probability and statistics), science (e.g., biochemistry), and a core set of problem-solving methods (e.g., computer algorithms) to the understanding of living systems.

Bioinformatics is the application of tools of computation and analysis to the capture and interpretation of biological data Bioinformatics is essential for management of data in modern biology and medicine The Bioinformatics toolbox includes computer software programs such as BLAST and Ensemble. Analysis of the human genome is one of the main achievements of bioinformatics to date. Prospects in the field of bioinformatics include its future contribution to functional understanding of the human genome, leading to enhanced discovery of drug targets and individualized therapy.

25

SINGLE CELL PROTEIN Rashmi Tyagi

Explosive population growth is a major problem of the world, particularly for the developing countries. Conventional agricultural practices are unable to supply sufficient food, particularly the proteins, despite increasing productivity. Through new agricultural practices high protein cereals have been developed. The use of processed microbial biomass, which are usually single-celled or filamentous in structure as the source of protein, is called single cell protein (SCP). The biomass is called single cell protein as it is rich in protein (more than 50% of the dry weight). The interest in SCP was generated to compensate for the protein deficiency, particularly in the developing countries. People have recognized the nutritional value of mushrooms, yeast, many bacteria and algae from the time immemorial, e.g. people from the Lake Chad in Africa and the Lake Texcoco in Mexico have been harvesting the blue-green alga, Spirulina, and using it as food after drying in sun. During the last three decades there has been a growing interest in using microbes for food production, particularly for feeding animals, poultry and in aquaculture for farming shrimps, prawns, fish,etc, which in turn would improve the human nutrition. SCP are easier to store and can replace the traditional protein supplements like fishmeal and soya meal. They are used as the protein supplement and to improve flavour for humans. Processing to degrade nucleic acids is required because metabolism of DNA and RNA yields uric acid which causes stones in kidney. The quality as well as the quantity of the proteins are the major goals of SCP production. In addition to proteins, microbes also contain carbohydrates, fats, vitamins and minerals. Many companies throughout the world have been involved in the production of SCP, and many products are commercially available, e.g. ‘Sunova’ capsule containing Spirulina is manufactured by Dabur company in India. Microorganisms produce proteins more efficiently than the farm animals, e.g. the doubling time for the bacteria and yeast is about 20-120 min, whereas, for a young cattle it is 1-2 months. Moreover, microbes can be more easily genetically modified for a desirable amino acid composition than the plants and animals. Microorganisms have relatively high protein content and the nutritional value of protein is also good. Microorganisms can be grown in excessive amount in relatively small fermentation bioreactors, particularly continuous cultures, all the year round where growth is independent of climate. Many of the microorganisms can be cultivated on a wide range of low value raw materials or waste materials, particularly low value waters which would help to reduce pollution. A unique aspect of SCP field is the problem of safety, nutritional value and acceptability of the product. The raw material used for the production of SCP is the main safety hazard, e.g, presence of carcinogenic hydrocarbons, heavy metals and other contaminants as well as the toxin production by certain fungi. Sanitation and quality control procedures must be maintained to avoid the contamination by pathogenic or toxigenic microorganisms. Toxicological testing of the final product must be thoroughly performed. In addition, the odour, taste and texture of the product is equally important. First industrial production of SCP, Candida utilis, occurred during World War I by Germany and was used in soups and sausages. A variety of substrates like inorganic carbon (e.g. CO2), industrial effluents (e.g. confectionary effluents, whey, molasses) and low cost organic materials (e.g. cellulosic wastes like straw, starch hydrolysate) are used for SCP production. The microorganism used for SCP production must be non-pathogenic, should have good nutritional value, can be easily and cheaply produced on large scale, toxin-free, fast growing and easy to separate from the medium. Some of the important microorganisms used for SCP production are: (i) Algae: Most commonly used algae are Chlorella (a unicellular green alga), Scenedesmus (a colonial green alga) and Spirulina (a filamentous blue-green alga) which are photosynthetic and are generally grown in open tanks or ponds. They utilize CO2, sunlight and a few inorganic nutrients for their growth. Algal SCP has about

26

60% crude protein having good amino acid composition. They are suitable for protein-rich feed supplement for animals. Chlorella and Scenedesmus have long been used as food in Japan while Spirulina in Africa and mexico. Chlorella is commercially produced in Japan to be used in yoghurts, ice-cream and breads, while Spirulina maxima in Mexico as animal feed. Spirulina is harvested by filtration. The major disadvantages of algae the are risk of contamination and costly recovery methods, especially for unicellular algae. (ii) Fungi: Some fungi used as SCP are unicellular (yeasts) whereas others are filamentous. (a) Yeasts: Members of Saccharomyces cerevisiae (Baker’s yeast), Candida utilis (Torula yeast) and Kluyveromyces fragilis are widely used as SCP. They have 55-60% protein with good amino acid balance and also rich in vitamin-B. They are used both for human food and animal feed supplementation. During their production, the risk of bacterial contamination is low and they are harvested by centrifugation. Saccharomyces cerevisiae is grown on molasses and is used commercially for fermentation of dough in bakeries; and thus eaten indirectly as components of food. Candida utilis is also used commercially in U.K., USA, Russia, Europe in soups and sausages and grown on various substrates, like confectionary effluents, ethanol and sulphite liquor. Kluyveromyces fragilis is basically grown on whey and is used commercially in France. The yeast secretes lactase enzyme which helps in the digestion of the milk sugar lactose into glucose and galactose. (b) Filamentous Fungi: The commonly used filamentous fungi as SCP are Fusarium graminearum, Chaetomium, etc. which are grown on starch hydrolysate and cellulosic wastes, respectively. They are usually grown as submerged cultures and have protein content of 50-55%. Harvesting of these fungi is rather easy by filtration. The main problem associated with these fungi are their slower growth, and contamination by yeast. Mushrooms are the fruiting bodies of certain large fungi belonging to the group Basidiomycetes and are rich in proteins, vitamins and other nutrients. Moreover, they are devoid of starch and are suitable for diabetic individuals. Agaricus bisporus is the common white button mushroom and accounts for over 70% of total mushroom production. It is grown on moistened paddy or wheat straw compost in wooden trays. After white cottony mycelial (filaments) growth the compost bed is covered with a 1-2 cm thick layer of soil and sand. The mushrooms (fruiting bodies) are harvested at the button stage. Lentinula edodes is the second most cultivated mushroom in the world and over 90% of its production occurs in Japan. Some of the other species of edible mushroom are Pleurotus and Volvariella. (c) Bacteria: A large number of bacterial species have been evaluated for SCP production using wide variety of substrates. They have very high growth rates and are used at commercial level, e.g. Methylophilus methylotrophus grows on methanol. They have over 80% protein. The risk of contamination by pathogenic bacteria is high during cultivation, moreover recovery is also problematic. They are recovered by flocculation and floatation combined with centrifugation. Sun-drying of SCP is cheap but it reduces its quality. Heat treatments are used during the final stages of harvesting to inactivate heat-sensitive organisms and to reduce RNA content. The biomass may be further processed or even the protein may be isolated and purified. SCP can be stored and shipped over long distances. SCP processes are mostly capital and energy intensive and most processes must be conducted under sterile conditions in expensive equipments. The future of SCP would depend on reducing production costs and improving quality. However, the main limitations for SCP products for human use are sociological and the major role will be in animal feed supplements.

Most of us have enjoyed the taste, flavour and softness of resilient chewing gums. We often watch cricketers, athletes and other sportsman on the field, chewing this rubber like sticky material. It is available in the market in different shapes, fragrances produced by renowned MNCs. One of the most popular brand is Wrigley’s chewing gum. Main ingredients of this materials are sugar, dextrose, glucose syrup, glycerin, emulsifier, antioxidant, variety of essential oils and ester based fragrances and gum base As chocolates or candies dissolve in the mouth, but gumbase don’t. It is a thickened resin and latex from certain kinds of trees. For centuries, the ancient Greeks chewed maotic-gum. This is the resin obtained from the bark of the maotic tree, a shrub-like tree. Grecian women specially liked this mastic gum to clean their teeth and sweeten their breath. In 1845, Mexican General Santa Anna while in exile in New York introduced chicle gum exudates of a plant, Sapodilla to Thomas Adams, an American businessman from New-Jersey, who began experimenting with it as a substitute of rubber. Adams tried to make toys, masks, and rain-boots out of chicle but every experiment failed. Anyway he liked the flavour and taste of that milky exudates of the plant, and one day he heated that material in a big vessel with sugar and transformed it into a semi-solid sweetened mass and then made it cut into small pieces and distributed among his friends and colleagues, the response was overwhelmingly good. The commercial production was carried out in a small factory in Brooklyn. And in 1871, Thomas Adam claimed patent for the same. Gum made with chicle and similar latexes soon won favour over spruce gum and paraffin gum. By the early 1900s, with improved methods of production, packing and marketing, modern Chewing-gum was well on its way to its current popularity. Although chicle and other natural gums are still utilized by the chewing-gum industry, some because of ever increasing huge demand, are being extended by synthetic materials like Poly-vinyl acetate (PVA) and other polymeric substances. Presently, Most chewing-gums are manufactured in the same manner upto a certain point. Basically the gum base is melted in large steam jacketed kettles at 2400F, at this point it achieves the thickness of maple syrup, which is then filtered through fine mesh screens, clarified in centrifuge and further filtered through fine vacuum strainers. Throughout the process the syrup is kept hot. Now ‘mixers’ which are huge vats and are equipped with slowly revolving blades powdering sugar, whose particle size has a definite effect on the brittleness, is added, then other ingredients like corn syrup, flavoring agents and also introduced. These contents are high quality, produced under hygienic, rigidly controlled laboratory conditions. Commercial production of chewing gum created enormous business to every sphere of industry, as production, quality control, packaging, marketing as well as advertisement. In its initial stage production was based on natural extract of specific trees, as demand increased scientists, researchers, found new synthetic Gum-bases, which are economically viable.

28

SUPERCONDUCTIVITY: A HISTORICAL VIEW Sunanda Vashisth

Superconductors, materials that have no resistance to the flow of electricity, are one of the last great frontiers of scientific discovery. Not only have the limits of superconductivity not yet been reached, but the theories that explain superconductor behavior seem to be constantly under review. In 1911 superconduc-tivity was first observed in mercury by Dutch physicist Heike Kamerlingh Onnes. When he cooled it to the temperature of liquid helium, 4 degrees Kelvin (-452F, -269C), its resistance suddenly disappeared. The Kelvin scale represents an “absolute” scale of temperature. Thus, it was necessary for Onnes to come within 4 degrees of the coldest temperature that is theoretically attainable to witness the phenomenon of superconductivity. Later, in 1913, he won a Nobel Prize in physics for his research in this area. The next great milestone in understanding how matter behaves at extreme cold temperatures occurred in 1933. Walter Meissner and Robert Ochsenfeld discovered that a superconducting material will repel a magnetic field (Figure 1). A magnet moving by a conductor induces currents in the conductor. This is the principle upon which the electric generator operates. But, in a superconductor the induced currents exactly mirror the field that would have otherwise penetrated the superconducting material - causing the magnet to be repulsed. This phenomenon is known as diamagnetism and is today often referred to as the “Meissner effect”. The Meissner effect is so strong that a magnet can actually be leviated over a superconductive material.

Figure 1

In subsequent decades other superconducting metals, alloys and compounds were discovered. In 1941 niobiumnitride was found to superconduct at 16 K. In 1953 vanadium-silicon displayed superconductive properties at 17.5 K. In 1962, scientists developed the first commercial superconducting wire, an alloy of niobium and titanium (NbTi). High-energy, particle-accelerator electromagnets made of copper-clad niobium-titanium were then developed in the 1960s, and were first employed in a superconducting accelerator in the US in 1987. The first widely-accepted theoretical understanding of superconductivity was advanced in 1957 by American physicists John Bardeen, Leon Cooper, and John Schrieffer. Their Theories of Superconductivity became know as the BCS theory - derived from the first letter of each man’s last name - and won them a Nobel prize in 1972. The mathematically complex BCS theory explained superconductivity at temperatures close to absolute zero for elements and simple alloys. However, at higher temperatures and with different superconductor systems, the BCS theory has subsequently become inadequate to fully explain how superconductivity is occurring. Another significant theoretical advancement came in 1962 when Brian D. Josephson, a graduate student at Cambridge University, predicted that electrical current would flow between 2 superconducting materials - even when a non-superconductor or insulator separates them. His prediction was later confirmed and won him a share of the 1973 Nobel Prize in Physics. This tunneling phenomenon is today known as the “Josephson effect” and has been applied to electronic devices such as the SQUID, an instrument capability of detecting even the weakest magnetic fields(Figure 2) The 1980’s were a decade of unrivaled discovery in the field of superconductivity. In 1964 Bill Little of Stanford University had suggested the possibility of organic (carbon-based) superconductors. The first of these theoretical superconductors was successfully synthesized in 1980 by Danish researcher Klaus Bechgaard of the University of Copenhagen and 3 French team members. (TMTSF)2PF6 had to be cooled to an incredibly cold 1.2K transition temperature (known as Tc) and subjected to high pressure to

29

Figure 2

superconduct. But, its mere existence proved the possibility of “designer” molecules - molecules fashioned to perform in a predictable way. Then, in 1986, a truly breakthrough discovery was made in the field of superconductivity. Researchers at the IBM Research Laboratory in Switzerland, created a brittle ceramic compound that superconducted at the highest temperature then known: 30 K. What made this discovery so remarkable was that ceramics are normally insulators. They don’t conduct electricity well at all. So, researchers had not considered them as possible hightemperature superconductor candidates. The Lanthanum, Barium, Copper and Oxygen compound that Muller and Bednorz synthesized, behaved in a not-as-yet-understood way. The discovery of this first of the superconducting copper-oxides (cuprates) won the 2 men a Nobel Prize the following year. It was later found that tiny amounts of this material were actually superconducting at 58 K, due to a small amount of lead having been added as a calibration standard - making the discovery even more noteworthy. Muller and Bednorz discovery triggered a flurry of activity in the field of superconductivity. Researchers around the world began “cooking” up ceramics of every imaginable combination in a quest for higher and higher Tc’s. In January of 1987 a research team substituted Yttrium for Lanthanum in the Muller and Bednorz molecule and achieved an incredible 92 K Tc. For the first time a material (today referred to as YBCO) had been found that would superconduct at temperatures warmer than liquid nitrogen - a commonly available coolant. Additional milestones have since been achieved using exotic - and often toxic - elements in the base pervoskite ceramic. The current class (or “system”) of ceramic superconductors with the highest transition temperatures are the mercuric-cuprates. The first synthesis of one of these compounds was achieved in 1993 by Prof. Dr. Ulker Onbasli at the University of Colorado and by the team of A. Schilling, M. Cantoni, J. D. Guo, and H. R. Ott of Zurich, Switzerland. The world record Tc of 138K is now held by a thallium-doped, mercuric-cuprate comprised of the elements Mercury, Thallium, Barium, Calcium, Copper and Oxygen. Dr. Ron Goldfarb at the National Institute of Standards and Technology-Colorado confirmed the Tc of this ceremic superconductor in February of 1994. Under extreme pressure its Tc can be coaxed up even higher - approximately 25 to 30 degrees more at 300,000 atmospheres. The Type 1 category of superconductors is mainly comprised of metals and metalloids that show some conductivity at room temperature. They require incredible cold to slow down molecular vibrations sufficiently to facilitate unimpeded electron flow in accordance with what is known as BCS theory. BCS theory suggests that electrons team up “Cooper pairs” in order to help each other overcome molecular obstacles - much like race cars on a track drafting each other in order to go faster. Scientists call this process phonon-mediated coupling because of the sound packets generated by the flexing of the crystal lattice.Type 1 superconductors - characterized as the “soft” superconductors - were discovered first and require the coldest temperatures to become superconductive. They exhibit a very sharp transition to a superconducting state (Figure 3) and “perfect” diamagnetism- the ability to repel a magnetic field completely. Below is a list of known Type 1 superconductors along with the critical transition temperature (known as Tc) below which each superconducts. Surprisingly, copper, silver and gold, three of the best metallic conductor do not rank in the superconducting elements. SomeType I superconductor are listed below Lead (Pb)

7.196 K

Lanthanum (La)

4.88 K

Mercury (Hg)

4.15 K

Tin (Sn)

3.72 K

Zinc (Zn)

0.85 K

Many additional elements can be coaxed into a superconductive state with the application of high pressure. For example, phosphorus appears to be the Type 1 element with the highest Tc. But, it requires compression pressures of 2.5 Mbar to reach a Tc of 14-22 K. The above list is for elements at normal (ambient) atmospheric pressure.

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Except for the elements vanadium, technetium and niobium, the Type 2 category of superconductors is comprised of metallic compounds and alloys. The recently discovered superconducting “perovskites” (metal-oxide ceramics that normally have a ratio of 2 metal atoms to every 3 oxygen atoms) belong to this Type 2 group. They achieve higher Tc’s than Type 1 superconductors by a mechanism that is still not completely understood. Conventional wisdom holds that it relates to the planar layering within the crystalline structure. Although, other recent research suggests the holes of hypocharged oxygen in the charge reservoirs are responsible. (Holes are positively charged vacancies within the lattice.) The superconducting cuprates (copper-oxides) have achieved Figure 3 astonishingly high Tc’s when you consider that by 1985 known Tc’s had only reached 23 K. To date, the highest Tc at ambient pressure has been 138K. One theory predicts an upper limit of about 200 K for the layered cuprates. Others assert there is no limit. Either way, it is almost certain that other, more-synergistic compounds still await discovery among the high-temperature superconductors. W. de Haas and J. Voogd fabricated the first superconducting Type 2 compound, an alloy of lead and bismuth, in 1930. But, was not recognized as such until later, after the Meissner effect had been discovered. L.V. Shubnikov in the Ukraine identified this new category of superconductors in 1936 when he found two distinct critical magnetic fields (known as Hc1 and Hc2) in PbTl2. The first of the oxide superconductors was created in 1973 when Ba(Pb,Bi)O3 was found to have a Tc of 13K. The superconducting oxocuprates followed in 1986. Type 2 superconductors - also known as the “hard” superconductors - differ from Type 1 in that their transition from a normal to a superconducting state is gradual across a region of “mixed state” behavior. Since a Type 2 will allow some penetration by an external magnetic field into its surface, this creates some rather novel mesoscopic phenomena like superconducting “stripes” and “flux lattice vortices”. While there are far too many to list in totality, some of the more interesting Type 2 superconductors are listed below by similarity and with descending Tc’s. Hg0.8Tl0.2Ba2Ca2Cu3O8.33

Introduction The first magnetic sound recorder was made by Danish inventor Valdemar Poulsen, when, in 1898, he passed the current from a telephone through a recording head held against a spiral of steel wire wound on a brass drum. Upon playback, the magnetic variations in the wire induced enough voltage (as amplification was not available at that time) in the head to power a telephone receiver. The hit of the Paris Exposition of 1900, Poulsen’s recorder won the grand prize. Development of coated magnetic tape began in Germany in 1928. The first tapes consisted of black carbonyl iron particles coated on paper, using a technique developed by Fritz Pfleumer to bronze-plate cigarette tips. By 1935, Badische Anilin und Soda Fabrik (BASF), a division of I.G. Farben, had produced cellulose acetate base film coated with gamma ferric oxide. During the war years, the tapes used for broadcasting were a suspension of oxide particles throughout the thickness of the acetate. In the 1950s, developments in magnetic recording diverged into separate, but related, paths, each growing within its own domain. The professional audio recording industry developed multitrack recorders, portable audio recorders, electronic editing techniques, and machine synchronizers that could speed lock one audio reproducer to other audio recorders, television recorders, or film cameras. The magnetic recording medium consists of a magnetic coating on some form of substrate. In the case of magnetic tape, the substrate is a flexible medium, such as Mylar, whereas in a magnetic disk drive it is typically an aluminum alloy or glass. To record and play back the information one or more magnetic recording heads are used. The recording head consists of a high-permeability magnetic core with a narrow gap cut into it and a few turns of conductor wound around it. When current flows through the conductor, magnetic flux flows through the magnetic core, emanates from the core at the gap and penetrates the magnetic medium, causing it to be magnetized to the right or the left. Binary data are encoded in the form of transitions (ones) or the absence thereof (zeroes) in the magnetization in coincidence with a clock, which is synchronized with the disk or tape motion. A similar recording head is used to sense the magnetic flux emanating from the recorded transitions in the medium during read back. In order to achieve high recording density it is imperative that the head be very close to the medium. Spacings of the order of 50 nm are used in today’s disk drives. Highly sophisticated signal processing electronics are used to encode binary ones and zeroes into the write current waveforms and also to convert the waveforms sensed by the read head back into digital data. An actuator is used to servo-position the head relative to the media for accessing the desired track of data. The rotation rates of magnetic disk drives today range from 3,600 to 10,800 rpm. With high performance actuators, it is possible to access a track on a disk in a couple of milliseconds. Hence, total access time to a random sector on the disk is only a few milliseconds, and disks provide relatively fast access to data. Magnetic tape drives on the other hand, record data linearly over the length of the tape. Average access time is the length of time it takes to transport half the length of tape over the head and is typically many seconds. Although tape has a relatively long access time, since it is very thin and can be wound upon itself, it offers an extremely high volumetric storage density and low cost. A relatively new technology in both disk and tape drives is magnetoresistive (MR) head technology. Previously, inductive heads, which sensed the time rate of change of magnetic flux in the head core, were used. However, inductive heads have limited sensitivity, and the amplitude of the read back signal depends upon the relative headmedium velocity. Magnetoresistive heads, on the other hand, are considerably more sensitive than inductive read heads, and since they directly detect the amount of flux flowing through the head core, the signal amplitude is independent of the head-medium velocity. Recently, IBM and Japanese manufacturers Yamaha and TDK have

Recording Almost all the magnetic properties of materials used in audio recording stem from the axial spins of the third shell of orbiting electrons of the atom. The electrical charge of the electron rotates, generating a current, which in turn generates a magnetic field. In nonmagnetic materials, electrons occur in pairs having opposing spin, canceling the magnetic effect. Iron, in particular, is heavily unbalanced, and nickel and chromium also exhibit magnetism. Compounds and alloys of these are useful in tape recorders. Applications include motors, transformers, loudspeakers, heads, tape, and shields. The crystalline structure of magnetic materials includes groupings of millions of atoms whose spin axes are aligned. Each group is called a domain and in effect is a tiny saturated magnet.The direction of magnetization can be reversed by the application of a strong opposing field. In demagnetized materials, the direction of magnetization of the domains is randomly distributed, resulting in a net sum of zero. The simplest recording system consists of a ring-shaped electromagnet with a ferrous core mounted over a ferromagnetic surface traveling at a velocity V. Since the core of the electromagnet is ferrous, the flux will preferentially travel through the core. Thus, the core is deliberately broken at an air gap. In the air gap, the flux will create a fringing field that extends some distance from the core. The signal current through the electromagnet generates a fringing magnetic field H. The fringing magnetic field H then creates a remanent magnetization on the ferromagnetic surface. Thus, the ferromagnetic surface now has become permanently magnetic. The magnetic particles in the surface act like little bar magnets themselves and create their own fringing magnetic field H above the ferromagnetic surface. Now, assume an analog signal into the electromagnet. The analog signal will create an analog variation in H. Since the surface is moving in time, then the analog variation of the signal in time is translated into a magnetic remanent variation on the surface in space. Thus, a very important number in magnetic recording is the spatial variation which corresponds to a signal frequency. If an incoming analog signal has a frequency f, then the characteristic wavelength of the pattern written on the magnetic media has a wavelength given by

It is important that the magnetic media chosen has a small enough spatial resolution to be able to support the desired frequency range at the given velocity. In many cases, the velocity may be increased in order to record the desired frequencies for magnetic media with lower spatial resolutions.

Reading The simplest reading system consists of the same head that was used to write the data on the ferromagnetic surface traveling at the same velocity V. The head now passes over the fringing magnetic fields H above the ferromagnetic surface. The voltage then induced in the electromagnet is proportional to the spatial (i.e. time, since the tape is moving) derivative of the magnetic field created by the permanent magnetization in the material

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e = induced voltage

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N = number of turns

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F = magnetic surface flux

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V = velocity

The Media A variety of magnetic media have been used over the years. In the very early recorders, ferrous wire- also known as “wire recorder”, was used. However, most modern magnetic media use a thin layer of ferromagnetic material supported by a non-magnetic substrate. The magnetic layer can be formed of magnetic particles (such as gamma ferric oxide) in a polymer matrix. Alternatively, the layer can be a vacuum deposited metal or oxide film. The use of a thin magnetic layer permits many possible configurations for the substrate. Audio recording is largely dominated by tapes, but drums and rigid disks are also used. Digital recording at one time was completely dominated by tapes, but today has moved to flexible or rigid disks. Magnetic media are differentiated into “hard” and “soft” media. Hard media require large applied fields to become permanently magnetized. Once magnetized, large fields are required to reverse the magnetization and erase the material. Such media, with large saturation remanence and high coercivity are appropriate for such applications as computer data storage. Soft media, on the other hand, require relatively low fields to become magnetized. These low remanence, low coercivity, materials are more appropriate for applications such as audio recording. The choice of the media influences the way the magnetization is recorded on the disk. Media with needle shaped particles oriented longitudinally tend to have a much higher remanent magnetization in the longitudinal direction, and favor longitudinal recording. This longitudinal orientation can then supported by a head design (such as a ring head) which promotes longitudinal fields. The result is longitudinally recorded magnetization. Similarly, media can be constructed with crystallites oriented perpendicularly to the field. Such media have a much higher remanent magnetization in the perpendicular direction, and favor perpendicular recording. This perpendicular orientation can then supported by a head design (such as a single pole head) which promotes perpendicular fields. The result is perpendicularly recorded magnetization. Particulate media The ideal particulate magnetic media has isolated long ellipsoidal particles suspended either longitudinally or transversely in a matrix. Particulate magnetic media are most commonly used in audio tape applications. In order to insure recorder and reader compatibility, the ac bias, signal current and frequency equalization have been standardized. Thus, the coercivity, remanence and thickness are essentially set by the standardization. Improvements in performance include such things as particle alignment and morphology. The most common magnetic material used for particulate media is an oxide of iron called gamma ferric oxide or synthetic maghemite (Fe2O3). Although elemental metals or alloys can be used, it is more difficult to control the morphology of metals than oxides. Elemental metals and alloys are better suited for film deposition. The magnetic particles for the media are usually suspended in a binder material. Great care must be taken when introducing the particles into the binder to avoid damaging them and ruining their elongated shape. A number of organic polymers are used for binders, including vinyl chloride, polyvinylchloride (PVC), methyacrylate, poly methyl methyacrylate (plexiglass), polyurethane, epoxy, polyamide and so on. The binder material must also include additives to reduce sedimentation and clumping. Additionally a solvent must be added to the binder to aid in deposition, and lubricating materials must be added to assure long tape life. This is especially important in applications (such as pause on a VCR) where the tape may be rapidly scanning.

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Substrates for tape or flexible media are typically polyester (terephthalate). Substrates for rigid media are usually aluminum. Aluminum substrates are usually coated with a reactive binder which both provides a base for polishing and lapping, and minimizes the change of corrosion from the metal. There are a variety of ways that the coatings are placed on the media. For flexible media, the coatings may be rolled on, using a processes called gravure, knife and reverse rolling. Following deposition, the magnetic particles are then oriented with an applied magnetic field. Film deposition In particulate magnetic films, the magnetization is created by particles (typically oxides) scattered through the film binder. In deposited magnetic films, the magnetization is typically created by metal crystals formed during the deposition process. Thus, there is less control over the morphology of the individual magnetic elements. As a consequence, film deposition of magnetic material did not reach the commercial marketplace until the mid 1980s — primarily in the form of Winchester hard-drives and high quality video tapes. The significantly higher density possible with metal deposited films has been an important feature in developing small high density computer hard drives, as well as smaller videotapes for portable video cameras. The majority of film deposition existing products use plated or sputtered Co-P or Co-Ni-P films on an Al-Mg substrate with a Ni-P undercoat and some type of protective overcoat. Typically, metal films are deposited in a multilayer process. The substrate is typically aluminum alloy with some sort of overcoat to increase surface hardness, reduce corrosion, and improve the adhesion of the metal film. The undercoat is followed by a thin coat of the magnetic material (typically 50-100 nm thick). This coat is followed by a protective overcoat. Number of techniques are used to deposit metal thin films, such as- Electroplating, thermal evaporation, e-beam evaporation, DC sputtering and RF sputtering. The details of these techniques are available in the previous volume of this departmental Journal ‘Vani’ of ITM, Gurgaon.

Mathematics is fundamental to study of virtually all science subjects and prerequisite for the study of many others. More and more careers need some knowledge of mathematics. Whether you are interested in becoming a linguist, geographer or psychologist, a share-broker, architect or market researcher, a computer programmer, physicist or biologist-mathematics opens doors! In addition, the demand for statisticians and for people who have a working knowledge of statistics has burgeoned in recent years. Statistics is an area of applied mathematics and is concerned with the collection, analysis and interpretation of data. Statisticians examine data and use it to draw conclusions about the nature of the data collection process or the population which provided it. Statistics form an integral part of many scientific research programmes, particularly in environmental, biological and social sciences. A distinction can be made between the various branches of statistics and the rest of mathematics. Mathematics is inherently highly precise, whereas statistics deals with variability and probability. In this article we include statistics under the umbrella of mathematics. Operations research: The study of which requires a good understanding of statistics, is the science of decision making in business, industry and government. This involves designing models for a system and then analyzing and optimizing these models. This process can be applied to resource allocation, inventory control, scheduling, optimal design and the operation of large-scale systems. Opportunities: Mathematics opens doors because it provides a critical knowledge base, enabling you to study subjects such as physics, chemistry, economics and engineering, and because it compliments and supports so many others. In the job market many employers consider it a plus if one or more maths papers are included in a degree, as this indicates a good level of numerical ability. The higher you rise in a career, the more likely you are to need management skills, which will include the ability to make decisions based on the analysis of numerical data. The study of mathematics will help to develop your powers of analysis, logical thinking and problem solving, and also help you think concisely and precisely, attributes needed for almost all careers. Your career prospects are therefore enhanced if you include mathematics in your degree.

Where do mathematicians and statisticians work? Mathematicians and mathematical statisticians are employed in a wide variety of organization, often as part of a multi-disciplinary team in which their particular expertise complements that of others. But by far the greatest use of mathematics is in various specialist applied areas such as statistics, operations research, biometrics (statistics for the study of biology), econometrics (statistics for the study of biology), econometrics (statistics for the study of economics) and in discipline which are highly mathematical in; nature such as meteorology (the study of weather and climate), geophysics (the physics of the earth), seismology (the scientific study of earthquakes), volvanoes (the scientific study of earthquakes), vulcanology (the scientific study of the material universe and the earth’s place within it), metrology (the science of weights and measures) and computer science.

Industry and Commerce: Graduates combining statistics, operations research, computer science, economics, management and other commerce subjects are in demand Manufacturing and processing companies and utility suppliers in the telecommunications, electricity, gas and petrochemical industries employ theoretical and applied mathematicians, operations researchers, statisticians and economists. The IT industry often recruits graduates from maths-related disciplines in addition to graduates from computer science and engineering. A general understanding of mathematics (particularly statistics) is very valuable in business services including marketing, market research, accounting, management and communications.

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Good mathematical skills are also advantageous in the construction industry: Mathematical calculations play a significant part in the work done by architects, technicians, engineers, quality surveyors and planners. Applied mathematics is used in all branches of engineering which include: civil, mechanical, electrical and electronic, chemical and process, natural resources, mining and forestry, engineering.

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Education: Schools, universities and other educational institutions employ teachers and educators at all levels. Applicant for teacher training with degree in mathematics, physics and related disciplines are particularly welcomed as there continues to be a shortage of new entrants to the profession in these subject areas.

Skills and personal to become a mathematician The skills and qualities listed below are often inherent talents but will be developed and enhanced through the study of mathematics. This is one reason why People who have studied mathematics are in demand. Numerical confidence: A prime requirement for all mathematical works is to be comfortable with numbers, their relative size and what they express. This includes notjust a mechanical approach but an ability to see when numbers make sense and are within the bounds of possibility. Quantitative skills: Many maths-related jobs require a good sense of quantity and its measurement. The ability to identify and measure quantities and develop or use relationships between the variables that the quantities represent is important. Problem solving: Mathematicians enjoy the challenge of wrestling with and solving problems, and of applying lateral thinking to finding solutions. Asking “what it?” They often use intuition and creativity to identify possible solutions to a problem. They will then apply their skills in logical thinking and analysis to systematically evaluate the relative merits of each solution. Computer literacy: Computers are used extensively in all statistical and most other mathematical work, so early familiarity with appropriate and current software is advantageous. Computer science courses should be included in a degree if advanced operations research courses are intended. Teamwork: Mathematicians are often employed as part of a team, in which different specialists are required to contribute their skills. It is important to be able to work well in a group. Communication and interpersonal skills: Mathematicians who can communicate complex information or ideas to their non-specialist managers, colleagues and clients are very valuable. It is also helpful if they can write reports in clear, jargon-free English.

Career in Mathematics There are some frequently asked questions regarding career in mathematics. 1. Why maths is considered to be a boring subject? Ans. Maths is a boring subject is just an illusion. Maths is very interesting and if taught properly students can enjoy it. If we look at mathematicians life we will find that they were interesting people. 2. Is it true that Indian mathematics students are in demand all over the world? Ans. It is true because even in the country like America the school level mathematics education is not so good. They really lack people who know mathematics and the person from country like India fulfill this requirement. So Indian students have very good prospects there. 3. Is there any necessity in India to make mathematics as a compulsory subject till graduation level? Ans. Again if we compare with country like America, there mathematics is compulsory before doing graduation in any field. In this modern age, mathematics should be studied till atleast class XII in India. 4. Now a days people are diverting towards vedic mathematics. Why is so? Ans. From ancient time India is the originator of number theory. Even today we can use it in progress of computer technology. 5. Is the level of school education in mathematics satisfactory? Ans. Before discussing about mathematics in India, let us take a look on the other countries. China, Germany and USA have very good level of education in mathematics, so is the case with small countries like Poland and Hungary. As said earlier level of school mathematics education in America is very poor although they try to compensate it in there university education. In India, level of maths which is taught in school is very good but the problem is with teaching techniques. Cramming the problems from books is not all about studying mathematics. Necessity is to develop active interest of subjects in the student of mathematics so that they not only enjoy the subject but also discover new formula and methods to solve any problem. 6. Is it necessary to join any coaching institute for preparing for IIT? Ans. In view of today’s competition, it is better to join some coaching institute but the key to success is of course your hardwork. Always remember, to read any subject self study and self analysis is most important. Do not depend completely on the coaching. Always join those classes where teachers help you to develop you thinking about the subject. 7. Now a days in which fields of mathematics the research work is going on? Ans. Today most of the research work is going on inter disciplinary area rather than pure mathematics. These new areas has more prospects in the future in India. 8. How one can make career in vedic mathematics? Ans. Some of formulae of 16 formula of vedic mathematics are of very high class. Some of the formula are used in increasing speed and efficiency of mathematics. But still there is lots more to explore in this field. 9.

What are the prospects of study abroad after completing B.Sc. (Hons.) mathematics from any Indian University? Ans. In America after completing school education, students goes for graduation for 4 years and then proceed to post graduation. Since in India graduation is for 3 years so Indian student can not take admission there. But after completing post graduation students can apply there. 10. There are many students who could not get through IIT, what are your suggestions for them? Ans. 1. While studying mathematics divide it concept wise, but take every problem of it as a new problem. There are unlimited problem in mathematics, but concepts are limited. So divide each topics into small topics according to concepts and then study it properly and solve maximum problems related to it. This will help student solve tricky and applied problems in IIT-JEE.

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11.

2.

Always solve the problem till you reach the final answer.

3.

Always make final notes for revision near examination time.

4.

Do not study much near examination time as it make the students more nervous. Nervousness to some extent increases concentration and alertness but beyond that it is very dangerous for students.

5.

Finally always take rehearsal exams seriously.

What are the career options after studying class XII with mathematics?

From the above table we can conclude that mathematics has a major role in each examination. The only exception is pre-medical examinations. India is among the very few countries where maths is not studied in medicine career. 12. After completing M.Sc. (Mathematics), how can a student do M.Tech.? Ans. The physics department of some universities (like D U) are conducing M.Tech in electronics and energy subjects. Student can qualify GATE examination conducted by IIT to do M.Tech from IIT in the field of maths and computer. 13. What is the role of mathematics abroad in different careers? Ans. The school education system of Britain is most advance. Almost in all major career there mathematics is necessary subject. Those careers in which maths is not required includes dance, drama or sports. Now a special note that in Britain every medicine related job has mathematics as a necessary subject. 14. How one can do higher studies in vedic mathematics? Ans. Though there is no definite university for it but there is university in America named as Brown university whose department of History of maths will be helpful in this area. In India too some people conduct these courses. 15.

What are the abilities which a student must have other than educational qualification to succeed in professional life? Ans. Without self confidence and positive attitude knowledge cannot be converted to success. Even if we fail we must have faith on our ability and hardwork. Always treat failure as a opportunity to learn more. 16. What is the use of mathematics in other fields of professional life? Ans. Industry : Stock control, allocation, Transportation, Queuing, Sequencing, traffic control, Linear & Non Linear Programming. Technology : IT, Network theory, Control system space Technology. Finance : Econometrics (Journals are purely mathematical), or, Linear Programming, Matrics & Linear algebra. Social Science : Social cybernetics, Mathematical Linguistics.

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Be this it can be said as we need a language to express ourself similarly mathematics is necessary in professional talks. Maths is not a subject but is professional language. 17 Is it necessary to study mathematics for being a doctor? Ans. In the age of information technology where each area is developed, medical science is also effected by it. Some of the applications of Mathematics also in medical science are Biomathematics

Today people are developing diagnostic software and artificial intelligence. For these field experts are required who can do mathematical modeling of human systems.

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A SHORT INTRODUCTION TO OPERATION RESEARCH Manoj Kumar Gupta

Origin & Development of OR The origin of the operation research, commonly known as OR, can be searched out many years back when our experts were trying hard for using a scientific technique in technical problems and in the managerial operations of the organization. It was the Second World War when the base of OR took place. During the Second World War, Britain had very limited military resources; therefore, in order to perform the various military operations in an effective manner, an urgent need of the tactful allocations of the limited resources was badly felt. Therefore, the higher military authorities formed a group of scientists to deal with the strategic and tactful problems related to air and land defence of the country by applying a scientific approach. As the group of scientists was involved in research on military operations, the job of this group was named as OR in Britain. Later on, United States, Canada and France were very impressed and encouraged by the tremendous success of the group of British scientists. The work of the group of scientists in United states were given various names like operational analysis, operations evaluation, operations research, system analysis etc. The success of OR in defence services drew the attention of industrial management in the new field. In this way, industry, business and government organizations were also very inspired by the success of OR in defence. After the war, several scientists were motivated to pursue research relevant to the field. The very first technique developed in this way in the field was called the Simplex method for solving linear programming problem and the credit to develop this important technique in 1947, goes to none other than the American mathematician George Dantzig. Since then many techniques known as the tools of OR like linear programming, dynamic programming, inventory theory, queuing theory etc are developed. Thus, we can easily observe the impact of OR in every walk of life.

Applications of OR OR is predominantly related with the approaches of applying scientific knowledge, besides the development of science. It equips the experts / managers with a better understanding to determine the better solution in his / her decision making problems with great speed, efficiency and confidence. Followings are some of the important applications of OR in the functional areas of management: 1. Finance, Budgeting & Investment i) Cash flow analysis, long-range capital requirements, dividend policies, and investment portfolios. ii) Claim and complaint procedure iii) Credit policies, credit risks and delinquent account procedures. 2. Personnel i) Estimating the human power requirement, recruitment policies and job assignment. ii) Selection of suitable personnel with due consideration for age and skills etc. iii) Determination of optimal number of persons for each service center. 3. Marketing i) Product selection, timing, competitive actions. ii) Selection of advertising media with respect to time and cost iii) Effectiveness of market research. 4. Physical Distribution i) Location and size of warehouse, distribution centers, retail outlets etc. ii) Distribution policy.

Drawbacks of OR Every of us are well familiar with the fact that every coin has two sides. This fact is also true about OR. We have just seen the some various useful applications of OR besides which we have also drawbacks of OR. Some of these drawbacks of OR are given below: 1. Sometimes the OR experts get too much lost in the model which they have built and forget the truth that their model does not represent the real world problems in which decisions have to be made. 2. There are several problems which a decision-maker may have to solve only once. in order to solve such problems, the construction of a complex Or model is often a very costly in comparison to the other les sophisticated techniques available to solve them. 3. Many of the OR models are so complicated that their solutions are next to impossible without the use of computer. 4. Sometimes the primary data are subject to frequent changes. In such cases, modifications of OR models can be proved a very costly affair.

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THE APPRECIATION OF POETRY Mona Malik

A poem is a moment’s monument, Memorial from the Soul’s eternity To one dead deathless hour. These lines by Dante Gabriel Rossetti very aptly and fully describe the nature of true poetry. Poetry begins in a stirring experience of the poet. It is conceived and composed in his soul. It involves a deep and insightful analysis and interpretation of his experience, and concretizes this abstraction into a beautiful real creation. Poetry is essentially a criticism of life. It makes us see the truth of our existence, our experiences; and does it so beautifully and subtly that we find the truth, not so much hard and saddening as elevating and chastening. Besides, we cannot but surrender to the delightful charm of its inventiveness – both in language and in representation of things. We cannot but marvel at the soulful memorial to one permanent, deathless hour in the poet’s past. Poetry has a distinct form which sets it apart from prose. This form is called “verse”, the essential characteristic of which is rhythm. All of us have heard the regular tramp of soldiers marching, the regular beat of the feet of people dancing. There is nothing like this regular swing in a prose passage. It is created by a poet’s arrangement of his words in such a way that the syllables(units that make up words) on which we naturally lay stress in speaking, come at regular intervals. The regular rising and falling in the flow of sounds in poetry, the recurring intervals of strong and light sounds like the beat of a drum, is called rhythm. Rhythmic verse is, generally speaking, the body of poetry. The soul of poetry, however, is constituted by four indispensable components, viz., verbal music, vision, imagery, and emotion. Verbal music: The poet instinctively chooses words of beautiful sound, and so arranges them that the words near each other will harmonize in sound. Besides, he sets them to a rhythm which suits the content of his lines and reinforces it. It is a combination of lovely rhythms with sweet-sounding words that gives poetry its peculiar music. Here are two verses from Dryden’s “Song for St. Cecilia’s Day”. The rapid rhythm of the first verse expresses the excitement caused by the war-alarm given out by trumpet and drum; the slow and quiet rhythm of the second verse suits the soft and tender music of the flute and lute. (a) The trumpet’s1 loud clangour2 Excites us to arms3, With shrill notes of anger And mortal4alarms. The double, double, double beat Of the thundering drum, Cries, Hark1! The foes2come; Charge3, charge, it’s too late to retreat. (b) The soft complaining flute, In dying notes, discovers The woes4of hopeless lovers Whose dirge5 is whispered by the warbling6 lute7 1) Trumpet: bugle, 2) Clangour: ringing noise, 3) Arms: weapons, 4) Mortal: deadly

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Poets frequently use a number of other techniques also to obtain some of the musical effects. These include (i) Rhyme (ii) Alliteration (iii) Repetition When words have the same vowel sound and end with the same consonant sound, they are said to rhyme. They give a pleasing musical chime. Rhymes may occur at the ends of lines and even within a line, for instance The ice was here, the ice was there The ice was all around; It cracked and growled8, and roared and howled9 Like noises in a swound10 Alliteration is a figure of speech which brings together words which begin with the same consonant sound, as in the following line A reeling11 road, a rolling12 road, that rambles13 round the shire14 The ‘r’ sound at the beginning of words lying close to one another produces alliteration. Repetition of words and phrases not only serves to emphasize the meaning, but often also to increase the musical effect of a poem. The western tide crept up along the sand And over and over the sand And round and round the sand. Vision: A great poet is a “seer”,i.e, a “see-er”; one who has spiritual insight and sees truths that others do not. He has, in moments of vision, the instinctive power of understanding things, their qualities and the relations between them, which ordinary people cannot see. All true poetry is the product of vision or imagination and is an expression of it. Wordsworth wrote a poem about a matter-of-fact, unimaginative man, called Peter Bell. Peter Bell saw nothing but what he saw with his physical eyes. He had no ‘vision’. A primrose by the river’s brim15 A yellow primrose was to him And it was nothing more. Now see what a primrose, or any common wild flower, is to real poet. Wordsworth himself says in his famous “Tintern Abbey” To me the meanest flower that blows can give Thoughts that do often lie too deep for tears. He finds even the simplest of flowers a manifestation of God’s spirit, of the divine principle that sustains all life. Imagery: The suggestion of vivid mental pictures, or images, by the skilful use of words, is called “imagery”. A poet can create or suggest beautiful sight-effects, as well as beautiful sound-effects by means of words. This capacity is part of his gift of imagination. His images may be drawn from the real world, or the ideal world of imagination in which he dwells. Poets have two ways of making us see mental pictures.

(a) By Description: He may describe a scene, real or imaginary, in words. Here is Emily Dickinson’s description of an imagined departure in a carriage with Death, of her final journey through her small world to the next: Because I could not stop for Death--He kindly stopped for me--The Carriage held but just Ourselves--And Immortality. We slowly drove--We passed the School, where Children strove At Recess-in the Ring--We passed the Fields of Gazing Grain--We passed the Setting Sun (b) By certain figures of speech such as simile, metaphor, and personification, in each of which the poet compares one thing with another, and so suggests some important point about it by an image. In a Simile a comparison is made between two objects of different kinds which have, however, at least one point in common. It is usually introduced by such words as “like”, “as”,& “so” O my Love’s like a red, red rose That’s newly sprung in June; O my Love’s like the melody That’s sweetly played in tune. A Metaphor is an implied simile. It does not state that one thing is like another or acts as another, but takes that for granted and proceeds as if two things were one, e.g, Life is a dream In Personification non-living objects and abstract notions are spoken of as having life and intelligence, e.g, Death lays his icy hands on kings and commoners alike Emotion: Ordinary prose writing (other than fiction) appeals more to the head than to the heart, but the function of poetry is to touch the heart, that is, to arouse emotion.Who can read such lines as these without emotion? For oft when on my couch I lie In vacant or in pensive mood, They flash upon that inward eye That is the bliss of solitude; And then my heart with pleasure fills And dances with the daffodils. It is only emotion that can rouse emotion. If the poet feels nothing when he writes a poem, his readers will feel nothing when they read it. Heart must speak to heart. To sum up, therefore, poetry springs from imagination roused by emotion, embodies a visionary truth, and is expressed in music and imagery. Poet is the priest of the invisible and poetry is his visible prayer.

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METALS AS A PART OF BIOLOGICAL SYSTEM Anupam Adhikary

There are about 40 elements, which take part in life processes of plants and animals and of these 25 are essential for human life. Few of them are Iron (Fe), Copper (cu), Zinc (Zn), Manganese (Mn), Selenium (Se), Cobalt (Co), Vanadium (Vn), Chromium (Cr), Potassium (K), Sodium (Na), Alluminium (Al), Molybdenum (Mo) and Calcium The important biological roles of the most essential metal ions can be categorize as follows 1) Fe2+ is a constituent of haemoglobin in blood, which carries oxygen to different parts of body .As average the human body, contains about 4 g of iron, of which 7% is found in haemoglobin. The haemoglobin acting as oxygen-carrier is the reversibility of the process. The oxygenated form of haemoglobin is known as oxyhaemoglobin while the reduced form is called deoxy-haemoglobin. This transfer of oxygen is remarkable, because it involves Fe2+ not Fe3+ Deficiency of iron causes anemia, breathing problem, poor appetite and retarded growth and development. However excess of iron causes the disease, siderosis, which is found especially in people who consume high ironical diet (a common disease in Bantu tribe of Africa who prepare their beer in iron pots. No physical impairment of lung function has been associated with siderosis. Inhalation of excessive concentrations of iron oxide may enhance the risk of lung cancer development in workers exposed to pulmonary carcinogens. The natural source of iron is spinach, red meat, liver kidney, Dried fruits, vegetables, wholegrain cereals and bananas etc. Copper and Zinc i) This essential trace element is required as a component of numerous enzymes, with between 1.5mg and 3mg necessary each day. The enzymes which it is a part of include:

ii)

CYTOCHROME OXIDASE – Takes part in energy production DOPAMINE MONOOXYGENASE – Necessary for neurotransmission in the brain SUPEROXIDE DISMUTASE – Protects cells from the damage which free radicals may cause CERULOPLASMIN – Converts iron from the form in which it is ingested to one which may be absorbed Copper is essential for the synthesis of haemoglobin and bone formation. Excess of this metal causes eminent health problems like ‘Metal Feaver’, flu like condition. Joint problems, and nervous disorder The body gets this metal by eating drinking water and even by breathing air because it is found prominently in nature and widely spread through environment. Food sources Good sources of copper include: Liver, Seafood, Nuts and seeds, Cereals, Vegetables, and Meat. Zinc is an essential constituent of many enzymes and maintains normal concentration of vitamin A in plasma. It is responsible for healing of wounds and the normal growth. Required for bodily functions such as vision, taste and smell Promotes normal function of cells and membranes, e.g. in connective tissue of skin Helps in the development and repair of tissue, e.g. in burn and wound healing Needed for bone growth Promotes healthy white blood cells and antibody production Involved in carbohydrate, protein and phosphorus metabolism Involved in insulin synthesis Food Sources: Meat, e.g. red and white Seafood, e.g. shellfish Liver, Eggs, Oats, nuts and seeds Hard cheese

2) Manganese is essential for normal bone structure, reproduction and normal functioning of the central nervous system. Manganese is one out of three toxic essential trace elements, which means that it is not only necessary for humans to survive, but it is also toxic when too high concentrations are present in a human body. When people

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do not live up to the recommended daily allowances their health will decrease. But when the uptake is too high health problems will also occur. The uptake of manganese by humans mainly takes place through food, such as spinach, tea and herbs. The foodstuffs that contain the highest concentrations are grains and rice, Soya beans, eggs, nuts, olive oil, green beans and oysters. After absorption in the human body manganese will be transported through the blood to the liver, the kidneys, the pancreas and the endocrine glands. Because manganese is an essential element for human health shortages of manganese can also cause health effects. These are the following effects: Fatness, Glucose intolerance, Blood clotting, Skin problems, Lowered cholesterol levels Skeleton disorders, Birth defects, Changes of hair colour, Neurological symptoms. 4) Chromium enhances the action of insulin in accelerating utilization of glucose in animal and humans. It is effective in improving glucose tolerance in patients suffering from diabetes. we are estimated to need between 50 to 200 micrograms of this trace element daily.Insulin become less effective in chromium deficiency with the result of impaired glucose tolerence. 5) Selenium: It is important for normal growth, fertility and for the prevention of a variety of animal disease. Selenium is a component of a number of important enzymes e.g. gluthathion peroxidase, which protect cells against attack by peroxide. Selenium compounds are absorbed by the human body and excreted as foul smelling derivatives in breadth and sweat. Humans may be exposed to selenium in several different ways. Selenium exposure takes place either through food or water, or when we come in contact with soil or air that contains high concentrations of selenium. This is not very surprising, because selenium occurs naturally in the environment extensively and it is very widespread. Selenium uptake through food is usually high enough to meet human needs; shortages rarely occur. When shortages occur people may experience heart and muscle problems. The exposure to selenium mainly takes place through food, because selenium is naturally present in grains, cereals and meat. Humans need to absorb certain amounts of selenium daily, in order to maintain good health. Food usually contains enough selenium to prevent disease caused by shortages. 6) Cobalt is an essential component of vitamin B12, which is necessary for normal RBC (red blood cell) formation. Cobalt is used to treat anemia with pregnant women, because it stimulates the production of red blood cells. Health effects that are a result of the uptake of high concentrations of cobalt are: Vomiting and nausea, Vision problems, Heart problems, Thyroid damage Health effects may also be caused by radiation of radioactive cobalt isotopes. This can cause sterility, hair loss, vomiting, bleeding, diarrhoea, coma and even death. This radiation is sometimes used with cancer-patients to destroy tumors. These patients also suffer from hair loss, diarrhea and vomiting. Cobalt dust may cause an asthma-like disease with symptoms ranging from cough, shortness of breath and dyspnea to decreased pulmonary function, nodular fibrosis, permanent disability, and death. Exposure to cobalt may cause weight loss, 7) Vanadium: Research has shown an association between V and improved insulin action, and that the minerals may also mimic the function of insulin. Vanadyl sulphate and sodium metavandate are being tested as anti-diabetic agents in clinical trials. It is present in the heart and blood vessels kidney, spleen, liver, bone and lung. Vanadium is thought to possibly have a role in normal iodine metabolism and thyroid function and may inhibit cholesterol formation in blood vessel the food sources are Fish, Mushrooms, Black Pepper, Canned Apple Juice. 8) Sodium: Sodium is a compound of many foodstuffs, for instance of common salt. It is necessary for humans to maintain the balance of the physical fluids system. Sodium is also required for nerve and muscle functioning. Too much sodium can damage our kidneys and increases the chances of high blood pressure. Contact of sodium with water, including perspiration causes the formation of sodium hydroxide fumes, which are highly irritating to skin, eyes, nose and throat. This may cause sneezing and coughing. Very severe exposures may result in difficult breathing, coughing and chemical bronchitis. Contact to the skin may cause

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itching, tingling, thermal and caustic burns and permanent damage. Contact with eyes may result in permanent damage and loss of sigh Food Sources: Obviously table salt is the main way which we gain sodium in the diet, however high amount are also contained in processed foods where the mineral acts as a preservative. 9) Potassium • A study showed that increasing the dietary K by supplements, in mildly hypertensive patients, lowered their systolic blood pressure significantly. • Research has found that an increase in the intake of K with calcium and magnesium, decreased blood pressure, therefore reducing the risk of hypertension and stroke. The exact mechanism is uncertain but possibilities include potassium’s ability to decrease platelet aggregation or reduce the total serum cholesterol. However… • A further study confirmed that an increase in dietary K lowered the blood pressure in hypertensive and normotensive patients but only if their initial intake of the mineral was low. It was also discovered that the blood pressure-reducing ability of K was compromised when combined with calcium or magnesium, indicating that they interfered with the blood pressure- lowering action of K. • Several other well-conducted studies also found that an increase in K in the diet resulted in a decrease in stroke mortality, but this association seemed to be more significant in black men and hypertensive males. Function Potassium is present in high concentrations in the body as an intracellular cation in all cells. It interacts with sodium (which is extracellular), via a sodium-potassium pump on all cell membranes, maintaining a membrane potential, and therefore conducting nerve impulses and also fluid balance. Most of the total body K is found in muscle tissue where it plays a major role in muscle contractions, e.g. regulating the rhythm of the heart in heart muscle. Because of its high concentrations in muscle cells, a measure of total body K can be used as a measure of lean body mass or cell mass, so that a decrease in total body K can indicate a loss of muscle mass. K exists in nature as three isotopes and it is the radioactive form, 40K, which is responsible for the body’s internal radioactivity and allows the total body K to be monitored. The values obtained can then be used as an indication of age (body K decreases with age), and disease. K is also present in blood serum, which is sensitive to dietary intake but not indicative of total body K. This small percentage of K present extracellularly is required for propagating electrical potentials between neurons, skeletal muscle function, and blood pressure homeostasis. Other functions of K include • Needed for enzyme-induced chemical reactions in cells • Helps maintain normal plasma levels • Reduces blood pressure • Converts glucose to glycogen for storage • Involved with hormone secretion • Helps in excretion of body wastes • Used to treat allergies • Promotes clear-thinking by helping to provide oxygen to the brain Deficiencies Low levels of total body K is not usually due to a lack of K intake from the diet, except in the case of starvation. However, K deficiency can result from a protein wasting condition in which the total cell mass of the body is decreased. Alternatively, hypokalaemia (low serum K), in which excessive K is lost from the body via urine,

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could occur as a result of using diuretics in hypertension treatment. In extreme cases, heart failure could be precipitated. Other symptoms of K deficiency • Nausea and vomiting • Listlessness, anxiety and nervousness • Muscle spasms, weakness and cramps • Rapid heart beat and hypertension • Constipation • Acne and dry skin Excessive intake: The excretion of excess K usually protects the body from accumulation of the mineral and therefore any toxicity. However, acute hyperkalaemia is lethal and possibly fatal by inducing cardiac arrest. Food Sources: K is present in most foods but the best sources are: • Fruits and juices, e.g. bananas, tomatoes, oranges • Green leafy vegetables • Whole grains and cereals • Meats and poultry • Potatoes • Water cress • Sunflower seeds • Dairy products (but not cheese) 10) Calcium: Calcium is the most common mineral in the body the majority of it is present in the bones and teeth, and a small percentage is found in the blood and soft tissues, e.g. in the heart and kidneys, where it is responsible for nerve impulses and muscle contractions. Ca has four main functions, some of which depend on the presence of other minerals • • • •

Structural (with phosphorus)- stores in the skeleton to maintain healthy bones Electrophysiological (with magnesium)-carries charge across membranes in an action potential, e.g. in nerve transmission; this is important in maintaining healthy CV function Intracellular regulator- participates in the protein structures of RNA and DNA Cofactor for extra cellular enzymes and regulatory proteins (hormones), e.g. those involved in digestion

Ca is therefore essential in the maintenance of life, affecting the genetic structure and mutations of cells in the body, and allowing the possibility of movement through its nervous functions as well as its role in determining healthy bones.

Other functions • • • • •

Helps to maintain a regular heart beat Regulates blood pressure with sodium, potassium and magnesium Important role in blood clotting Needed for muscle growth Aids with iron metabolism in the body

Deficiencies Acute symptoms of Ca deficiency are rare because Ca is usually taken from the vast skeletal stores for the body’s functional need However, chronic dietary deficiency of Ca may consequently result in rickets (in children) and

Excessive intake: This is usually due to over supplementation for therapy. If more than 2500mg of Ca is taken in a day, hypocalcaemia may overwhelm the kidneys and result in an increased risk of kidney stones and therefore urinary tract infections

The Dark Holds no Terrors1 is the story of a successful doctor, Sarita who is married to Manohar, an English teacher. The novel begins with Sarita (Saru) returning to her parental house after fifteen years, a place to which, she had sworn once, she would never return. The unbearable circumstances at her home where she lived with her husband and two children force her to return to her parental house. The narrative of the novel from then on vacillates from the present (Saru’s return) to the past (memories of her past) and vice-versa. While living in her father’s home Saru gets a chance to reflect on all the events of her life and remembers her childhood and the time she has spent in company of her younger brother Dhruva, his death, her domineering mother, Kamalatai, her marriage with Manu, her two children and her suffering in marriage. Right from her childhood, Saru has been subject to gender discrimination. Her mother always considered her inferior to her brother Dhruva. Dhruva would always get everything he wanted and she would not get what she wanted on the simple pretext that he was a boy. “He is different. He is a boy”2, she would say. She grows up an unloved and neglected child. Saru had once written in her notebook “ nobody likes me. Nobody cares for me . Nobody wants me….”3 The problems that Saru had been facing since her childhood become worse after her brother Dhruva’s death. Saru’s mother blamed her for Dhruva’s death and continuously cursed her for the same. “Why didn’t you die? Why are you alive when he is dead?”. 4 Shashi Deshpande in The Dark Holds no Terrors highlights the fact that in most of the cases of exploitation of women, women are the ones who are generally responsible for such exploitation. Kamalatai does not want Saru to study because she feels that eventually Saru has to get married and there is no point wasting money on her studies. Right from her childhood Saru has been told that her ultimate goal in life is to get married, so her entire energy should be concentrated in that direction. Saru and her mother hate each other. “If you are a woman, I don’t want to be one”5 says Saru to her mother. Kamalatai is terribly against her studying medicine. She feels that it would be very difficult to find a match for an ‘overqualified’ daughter. But Saru is hell-bent on joining a medical college and can do so after persuading her father a great deal. Saru succeeds in moving out of her house for the first time though only to be cursed by her mother. Saru wants to work hard and be a success, so that she can be secure and no one can ask her again “why are you alive?” .6 Saru was always uncomfortable because of norms set by the patriarchal society and thus wanted to run away from her home, her mother and all that signified bondage. She feels immensely relieved when she leaves her home to stay in the hostel to pursue studies in medicine. When she marries Manohar, she breaks all the shackles and boldly defies her family and the society by marrying out of caste. She is unlike the typical Indian woman who cannot summon up enough courage to face the society. But Kamalatai disowns Saru as she is utterly disgusted at what Saru has done. She retorts on being asked about her daughter- “Daughter? I don’t have any daughter. I had a son and he died. Now I am childless…. I will pray to God for her unhappiness. Let her know more sorrow than she has given me.”7 Saru the ‘lady doctor’ is a professional woman who is earning more than her husband. Manu is a typical patriarchal character who is neither very successful in life, nor is happy in letting his wife be more successful than he is. This economic independence and social superiority bring in Saru’s life innumerable problems. Manohar’s male ego is not able to digest the fact that his status and earnings are less than his wife’s. Saru realizes quiet early in the novel that this situation would lead to marital discord as well: “a + b they told us in mathematics is equal to b + a. But here a + b was not, definitely not equal to b + a. It became a monstrously unbalanced equation, lopsided, unequal, impossible.” 8

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A journalist once asked Manohar – “How does it feel when your wife earns not only the butter but most of the bread as well.”9 A typical male is not used to being asked such question as even till date the society has not become progressive enough to allow a typical male to react positively to such remarks. An unfortunate situation arises in a household when women speak on behalf of men and speak as patriarchs. These women have engrained in themselves all the patriarchal values and feel that it is their responsibility to train all females to follow this direction. They feel that rebels like Saru meet a terrible fate and they get what they rightly deserve. Kamalatai’s remark on the situation of a neighbour who had been tied to a peg in the cattle shed and fed on scraps like a dog hints exactly at this situation: “But how do we know what she had done to be treated that way? Maybe she deserved what she got!”.10 The neighbour had died after ten years of such suffering. Saru has been constantly told that she has to get married one day and that she cannot live with her parents for ever, “we have to get you married” 11. She is reminded again and again that she should not play in the sun, as she may get “even darker” .12 Deshpande is highlighting another aspect of the patriarchal society that a girl child is trained right from the beginning that she has to leave her parents house one day and till that day she has to preserve her beauty so that she is able to get a good match. Saru has been taught that her parental home is not hers. Her home is her husband’s home. But after a few years of her marriage, Saru realizes that just like her parents home was not hers, the place where she was living together with her husband was also not her own home.” No she couldn’t call it home. It was not home. Nor was this home. How odd to live for so long and discover that you have no home at all!”13 Saru has been made to learn by her parents that ‘a wife always be a few feet behind her husband”. 14 She despises the fact that throughout their lives, women in our country are taught that everything in a girl’s life is shaped to a single purpose of pleasing a male. Since time immemorial it has been socially accepted that man is the master and woman is his inferior and subordinate partner. ‘Manu’, the ancient law-giver, states: “Even though the husband be of bad character and seeks pleasure elsewhere he must be constantly worshipped as a God by a faithful wife.”15 The importance of economic independence of women is one of the chief concerns of the novel. Right from her childhood, Saru understands the importance of economic independence for women. As a child she had witnessed the plight of her grandmother who had been deserted by her husband and was considered a burden by the rest of the family. Our society has since ages: “deprive[d] the woman of education , dooming her to household chores only , especially service of her husband and in - laws…”16 Saru is not like her grandmother who suffered silently in the name of fate and luck. She knows that nothing is written on one’s forehead. Through her experiences, Saru has realized that women have been belittled and denigrated in the patriarchal setup and she vehemently protests against the existing notions. As a doctor she feels that “Indian women had schooled themselves to silence.” 17 She feels that they are “stupid silly martyrs... idiotic heroines. Going on with their tasks, and destroying themselves in the bargain.”18 She wants them to speak and fight for themselves so that they can survive in this world with dignity. She wants them to be treated like human beings, human beings who feel, who have their own share of sorrows and joys and human beings who have the right to live the way they want to and not according to the way the merciless world wants them to. Saru has the ability to reject what she is not comfortable with. She defies traditional codes set by the society without any inhibitions. She leaves home twice in the course of the novel, once when she leaves home to study

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medicine staying in the hostel and the second time when she leaves Manohar and her children in search of her home. But Saru realizes that running away from problems will not provide a permanent solution. She realizes that the real solution has to come from within one’s own self. The epigraph of the novel states what Saru has realized at the end of the novel: “You are your own refuge; there is no other refuge. This refuge is hard to achieve” Shashi Deshpande has in all her novels tried to give modern Indian women a voice through her simple plots that revolve around the ordinary lives of ordinary female protagonists. The protagonists in her novels experience a number of hardships in their lives and are women who, through these hardships learn to survive with their head held high. Mukta Atrey and Viney Kirpal observe – “…the protagonists develop from anxious unhappy, unassertive women which they are at the beginning of the narrative into mature , awakened , assertive women who understand and perceive the gender politics of socialization and need to break its shackles. They also recognize the need to make their choices as free women and human beings.”19 Deshpande’s main concern in her novels is to present the condition of women in the male - centered Indian society. In her novels she: “defines freedom for the Indian woman within the socio-cultural value system and institutions. She has steadfastly resisted the temptation of creating strong, glorified female heroes, and has presented the Indian women as facing the very real dilemma of having to choose between modernity and convention.”20 Shashi Deshpande in an interview states – “In a way my own writing is an attempt to break that long silence of women in India”21 The inequities against which women allover the world are trying to fight since ages are-legal economic and against social. After years of carrying the burden of her role in her brother’s death she finally talks to her father about it .She also finds the courage to tell him about her suffering in her marriage. This unburdening of her heart to her father brings to her much satisfaction. In the end she realizes that the dark no longer holds any terrors for her. She now does not want to run away from it, rather she wants to face it. The Dark Holds no Terrors represents the suffering and anguish of an Indian woman who is subject to all kinds of ill-treatment by her husband by the society and at times even by her parents. Shashi Deshpande has successfully tried to highlight all that a modern woman has to go through in this male-dominated society. According to K.M.Pandey: “Unlike other women who bear suffering like the torture of Sisyphus, she gathers strength not to surrender, not to run away from the problems, not to commit suicide not to be behind the symbolic purdah or veil - in a word not to accept defeat. Rather she accepts the challenge so as to prove herself a good daughter, a good wife, a good mother a good doctor and a good human being-not from the phallocentric point of view but from her own ‘female’ point of view”22 At the end of the novel her father advises her against running away “Don’t turn your back on things again. Turn round and look at them.”23 Saru heeds to the advice sincerely and decides to give life another chance. The Dark Holds no Terrors is thus the story of a modern woman Saru, who after having suffered various atrocities comes up victorious in the end. She did not submit to her ‘fate’ and circumstances. She revolted against the peripheral functions assigned to her and fought in her own way for a meaningful life.

SYNTHESIS AND STUDIES OF OPTICAL PROPERTIES OF POLY BISPHENOL-A-CARBONATE-GRAFT POLYMETHYL METHACRYLOYL HYDRAZIDE: THE PHOTOACOUSTIC SPECTROSCOPY Hukum Singh Introduction Thermoset materials like PC cannot be easily subjected to their melt processing to fabricate these into articles. Thermoplastic materials like PMMA on the other hand require low processing temperatures due to which they are conventionally processed into the articles. Thus graft co-polymerization of thermo-plastic material make suitable to latter for their melt processing. Further graft polycarbonate having Polymethylmethacrylate hydrazide linkage may be useful as a high temperature resistant material for aerospace and other defence applications. Extensive literature revealed that no such attempts were made to synthesize the graft polycarbonate having such hydrazide linkage. Therefore in the present work, we have made efforts [1] to synthesize the Polyhydrazide grafted polybisphenol-A-carbonate (PCGH) through condensation of (PMMA-G-PC) 50% and N- [p-(carboxyphenyl amino acetic acid) hydrazide (PCPH) and have studied its optical property by using PAS technique.

Synthesis of Graft Copolymers In a three necked flask (250 mL) equipped with dropping funnel mechanical stirrer and air supply tap was placed polybisphenol –A- carbonate 0.5 g potassium persulphate (40 mmol lit-1) thiourea (30 mmol lit-1) and aqueous nitric acid (100 mL, 0.18 M) was introduced followed by initiator potassium persulphate (KPS) to a well dispersed polybisphenol –A-carbonate (0.5g) in 100 ml of water with continuous stirring at 45+20C. To this was added methylmethacrylate (0.036 mole lit-1) drop wise to the reaction mixture at 1500 rpm for 3.0 h. At the end of the reaction, excess of methanol was added to quench it. The graft copolymer was purified through its repeated extraction with acetone using soxlet extractor to remove the homo polymer formed during the reaction. The graft copolymer was isolated and dried at 50 0C.

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Synthsis of PCGH PMMA-G-PC (0.5 g) was refluxed with (0.015 mole, PCGH) in N, N Dimethyl acetamide (25 mL) at 2000C for 4.0 h. The Polybisphenol-A-carbonate –graft Polymethylmethacrylate hydrazide (PCGH) were isolated by their precipitation with water, they were filtered and washed with ethanol and dried at 500C the FT- IR (Fig. ) and photoacoustic spectra (Fig. ) of compound is shown Experimental The schematic diagram of a single beam photoacoustic spectrometer designed and developed in our laboratory that used to record the photoacoustic spectra of the samples is shown in Fig.1[3]. The photoacoustic spectra of all compounds were obtained in the range of 200 – 800 nm regions. A 300 watts high pressure Xenon arc lamp (Model 68083, Thermo Oriel Corporation, USA) was served as an excitation sopurce. The white light was modulated at 22 Hz by a mechanical chopper (SR 540 Stanford, USA). The light was focused through a quartz lens of focal length 4.5 cm on the entrance slit of 1/8 m Monochromator (Cornerstone 130 Model 74000, Thermo Oriel Corporation USA) which was monitor by computer using the software’s (TRACQ 32 and monoutility program). The dispersed light from monochromator was focused by using quartz lens of focal length 5.0 cm on an indigenous PA cell (2.0 cm diameter, 2.0 mm depth). The acoustic signal was detected with condenser microphone (Radio Shake, USA) mounted in the PA cell. The output of microphone was amplified by preamplifier and then finally fed to a lock-in amplifier (SR 530 Stanford USA) for digital output display of amplitude and phase angle. The reference signal was provided to lock-in amplifier from the chopper for phase sensitive detection. The time constant of the lock-in amplifier in the present study was 30 seconds. Since the intensity of light output from Xenon arc lamp varies over the spectral region of interest, the PA signal from sample was normalized against a totally light absorbing reference sample like carbon black. In the present study the normalization was performed by dividing the amplitude the amplitude of PA signal of the sample by the amplitude of PA signal obtained from the carbon black sample.

RESULTS AND DISCUSSION Thermoset materials like PC cannot be easily subjected to their melt processing to fabricate these into articles. Thermoplastic materials like PMMA on the other hand require low processing temperatures due to which they are conventionally processed into the articles. Thus graft co-polymerization of thermo-plastic material make suitable to latter for their melt processing. Further graft polycarbonate having Polymethylmethacrylate hydrazide linkage may be useful as a high temperature resistant material for aerospace and other defence applications. Extensive literature revealed that no such attempts were made to synthesize the graft polycarbonate having such as hydrazide linkage. Therefore in the present work, we have made efforts to synthesize the Polyhydrazide grafted polybisphenol-A-carbonate (PCGH) through condensation of (PMMA-G-PC) 50% and N- [p- (carboxyl phenyl amino acetic acid) hydrazide (PCPH) and have studied its optical properties by using PAS technique. The synthesis of PCGH is represented by stepwise reaction is shown in Figure (2). To explain the absorption spectra of PCGH, it is necessary to have the PA spectra of its constituents {PCPH and (PMMA-G-PC) 50%}. Therefore in the first step PA spectra of PCPH along with its constituents (4-Aminobenzoic acid, N- [p- (carboxyl amino) acetic acid] have been recorded and shown in Figure 3. It clear from Figure 3 that the PA spectra of 4Aminobenzoic acid gives two clear absorption bands at 270 nm and one at 310 nm. Saturated carbonyl compounds like acetones exhibit three bands: a weak band around 280 nm, a more intense band around 190 nm, which are assigned to the n *, n * transitions respectively. The n * transitions of a large number of carbonyl derivatives have been reported in the literature [4]. The band at 270 nm indicates the presence of – COOH- linkage [5]. The present compound (4-Amino benzoic acid) which have auxochromic group (-OH) directly link with the –C=O- center due to which the (C=O) absorption band at 190 nm shifted at 270 nm. The second band at 310 nm is attributed due to presence of –NH2- linkage [6]. When the two substituent are of complementary type (Ortho-para directing verses m-directing) a very large bathochromic shifts of 200 nm occurs. Complementary

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disubsitution seems to have greater effect in the para position [7]. In case of N- para carboxylic phenyl amino acetic acid absorption at 370 nm are observed and Phenylalanine gives absorption band at 250 nm [8]. Comparison of the of N-carboxylic phenyl acetic acid with Phenylalanine renders that the former can be considered as para carboxyl derivatives of latter. Since a large bathochromic shifts of 200 nm was observed due to presence of complementary group. Therefore a band at 250 nm in p-carboxyl phenyl amino acetic acid is found to be shifted at 370 nm. Which is a bathochromic shift of around 120 nm. The band at 270 nm is N- [p-carboxyl amino) acetic acid] is due to the absorption band of carboxylic group, which was also observed in 4-Aminobenzoic acid. The PA spectra of hydrazide derivative of N - [p- (carboxyl amino) acetic acid] (PCPH) indicate missing absorption band corresponding to –COOH- group at 270 nm. This is because in PCPH free carboxylic is absent. Further PCPH showed a wide band around 250 nm. Semicarbazides shows absorption band at 230 nm [9]. This indicates that the absorption at 250 nm, in PCPH is due to hydrazide linkage. The very weak absorption band at 290 nm in PCPH may be due to trace amount of residual para amino benzoic acid remained unreacted during the synthesis of hydrazide. Similar residual band is also appeared at 300 nm for compound N- [p-carboxyl amino) acetic acid]. In the second step Photoacoustic spectra of pure PC, pure PMMA and PMMA-G-PC (50%) are recorded in solid phase and are shown in Figure 4. It is clear from Figure 4 that pure PC and pure PMMA shows absorption bands at 290 nm and 270 nm respectively. The peak at 270 nm in the PA spectra of PMMA may be attributed to the * transition of C=O bond [10]. The PA spectrum of (PMMA-G-PC) 50% shows strong band at 282 nm and its n signal strength is large in comparison to Pure PC and PMMA. As the peak at 282 nm in 50% graft copolymer lies in middle of the peaks of PMMA (270 nm) and PC (290 nm). The experimental observation clearly demonstrates that PAS technique is able to characterize graft copolymer having similar groups in their backbone and side chain. In the final step the PA spectra of PCPH, (PMMA-G-PC) 50% and PCGH are recorded in a similar condition as in step 1 and 2 and is shown in Figure 5. It is clear from the Figure 4.4.6 that the PA spectra of PCGH is very similar to the PA spectra of PMMA-G-PC, as PCGH shows a absorption band at 280 nm, similar to (PMMA-G-PC) 50%. This is because the backbone of PCGH and PMMA-G-PC are made from similar bisphenol-A linkage as repeating unit. Condensation of PMMA-G-PC with PCPH resulted PCGH, having hydrazide linkage as a side chain in the graft copolymer named as a polybisphenol-A-Carbonate–G-Polymethylmethacrylate hydrazide. FT-IR a spectrum is shown in the Figure 6. Structure of the proposed side chain in PCGH has also been confirmed by PA spectra (Figure 5 where similar trend in the PA signal of PCPH and PCGH are observed around 290 - 330 nm. The FTIR spectrum of PCPH and PCGH shows C-H bending absorption at 1950 cm-1, C-O stretch absorption at 3100 cm-1. It is clear from Fig. 4.4.7 that there is no apparent change in the absorption frequencies in FTIR spectra of PCPH and graft copolymer (PCGH) except their respective transmittance profiles. The overall transmittance of graft copolymer was increased in comparison to PCPH. This result shows that the graft product becomes transparent which has been confirmed by its physical appearance and also by PAS technique. It was concluded from above observation that FT-IR spectroscopy is apparently not found to be applicable to characterize these graft copolymers having similar groups in their backbone and side chain. The overall absorption of electromagnetic radiation in PC, PMMA-G-PC and PCGH has been ascertained through the height of PAS signals. The lower values of PAS signals have been assigned to transparency of the sample. In this connection, the graft co-polymerization of PMMA on to PC increased the PA signal intensity from 0.5 to 1.7 mv (Figure 5. This indicates that the graft co-polymerization of PMMA onto PC reduces the transparency of latter. Condensation of PCPH with PMMA-G-PC surprisely reduced, the PAS signal from 1.7 to 0.8 mv. The above results reveal that PCGH is more transparent then (PMMA-G-PC) 50% and such result is also observed in FTIR (Fig. 6). The heat resistance of a material depend on the cohesive energy of the bonds [11] Among this series the –COOH- linkage indicate the highest value cohesive energy correspond to high M.P. [11]. Introduction of hydrazide linkage in the same way may increase the melting point and hence heat resistance of the PCGH. From these observation it has been regarded that PCGH indicated high heat resistance, slightly reduced transparency than its parent polymers. Therefore the materials like PCGH may be utilized an aerospace material for defence purchase.

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Conclusion We have successfully studied the optical properties of polymeric samples and their derivatives using photoacoustic technique. It is clear from above discussions that conventional spectroscopy was unable to characterize PMMA-G-PC copolymers whereas PAS technique may be used efficiently for the characterization of these copolymers. Our results clearly demonstrate that PAS is capable of monitoring the polymerization of pure PC into grafted polycarbonate. Thus the study of the materials like 4-aminobenzoic, N- [p- (carboxyl amino) acetic acid, PCPH and PCGH this method is more suitable because this technique is; very quick, it require no sample preparation, it is non-destructive etc.

Globalization is forcing many organizations to change as it brings with itself cut throat competition. If Globalization is to become one of the central facets of organization, the role of the human resource function, department, and managers must be redefined in the context of this change. HR strategies can play more influential roles in global organizations than it has in the past. In light of theses developments the HR practices are changing as it has become a matter of survival. It is observed that the best practice companies recognize a link between improvements in workforce productivity and the HR strategies/practices of the organisation. Due to globalization, many organizations are moving towards HR strategies/ practices that are global in nature cutting across the culture of any one country. Global companies face a lot of differences in management style due to the differences in the culture across the globe. In any organisation there are three key productivity levers which can be identified. Theses are:

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Staffing / Recruitment / Employment

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Learning and Organizational Development

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Compensation

Staffing / Recruitment / Employment Staffing / Recruitment / Employment is an important function in any organization. A big part of the management conundrum is about people – knowing what you need, how to find the best people and help them achieve their best potential for the benefit of the business. Employees with the right attitude can make a lot of difference to any organization. While many corporations are still looking for skills and experiences, a growing number of organizations are no longer sticking with this traditional thinking concept. There has been a shift in the recruiting attitude from last decade. Many organization today employ candidate with right attitude coupled with the right knowledge. Now a days recruitment is done in such a way as to identifying professional attributes or competencies of the individual that is important to the organization and to see if there is a alignment in the strategy, corporate values and business objectives of the organization with the candidate. This provides higher likelihood of successful hiring decisions; increases potential for job satisfaction; improve retention; reduces turn-over. This has become necessary else there will be a high attrition rate( about 40% in some) which has become a night mare for few organizations. Though the reasons for attrition are quite different but if the recruitment process is attuned to the right attitude turnover can be lowered. A straightforward concept has gained importance- hire the right people and build a better and more profitable organization. Companies hiring for attitude, reason that you can teach the right person the skills to do the job but you can’t transform even the most knowledgeable person into a success if he/ she lacks the right temperament not surprisingly, hiring for attitude is especially popular in service-based industries and jobs that require customer contact. Global organizations today are recruiting ‘like-minded people’ so that there is a culture fit, i.e., match between the values of the organization. Organization now a days are aiming at socialization its employees through training and personal interaction. Examples • Southwest Airlines has built an entire corporate culture predicated on this concept. The Dallas-based carrier, which earned $5.5 billion in 2002 and employs nearly 34,000 people, spares no effort to find the perfect blend of energy, humor, team spirit and self-confidence. The first step in its hiring process is to take a group of applicants into a room and observe how they interact. Southwest feels that during the interview it’s not

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•

necessarily that a candidate gives the right answer but more important is the way a person answers. Southwest hopes that by the time the process is over, it will have identified the candidates who thoroughly fit its criteria. (www.workforce.com) UPS prides itself on finding people who fit into its culture and project the company image to its customers package-delivery service.

Companies like Southwest Airlines and UPS that eventually create a “brand” culture realize yet another benefit: they attract throngs of like-minded applicants who see themselves as a good fit. People who match the culture are attracted to it, and as applicants participate in pre-interviews and interviews, those that don’t feel comfortable drop out of the picture

Learning and organizational development helps in leveraging training to socialize an employee to the company vision, values, culture, nature of the business and organizational fabric, in providing guidelines for individual behavior, performance and understanding of the company business and values and in facilitating cultural change through the development of continuous improvement and continual learning organizations. This results in promoting shared organizational vision and a focus on aspects of performance most critical to the business. Learning and organizational development builds and uses a continual learning organization model. It uses training to help create a strategic advantage, with training goals aligned to the business strategy and competency models, in order to support the business objectives. It also develops training based on performance measure assessment. This results in positioning the organization to learn from mistakes and successes; builds an adaptive, flexible workforce Examples • Motorola promotes “competition” among process improvement teams and insists that most of its employees have a certain number of hours of training per year. In 2002, Motorola initiated Motorola’s functional learning teams, referred to as “domains.” For this Motorola employs thousands of engineers, and the domain was weakly aligned with the key business needs of the engineering community. (www.clomedia.com) • Ciba Gergy utilizes a competency model training approach, in which specific training is developed for specific levels of management • Met Life tracks outcomes and continuous improvements of training programs Learning and organizational development encourages the use of strategic technology to enhance training opportunities. This result in reducing the training costs; decreases reliance on classroom instruction; compresses training time; supports more cost effective Just In Time (JIT) training . For example Ernst & Young’s interactive desktop learning allowed the firm to reduce classroom days by more than 60% Learning and development uses action-learning approach to training, to integrate business issues and learning opportunities to solve real business problems. This results in utilizing adult learning principles; focusing on job-

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related issues and measuring effectiveness against actual business outcomes. Many organisation are now initiating new approaches like change management in their organisation. Learning and organizational development helps all theses ideas and concept to be assimilated and implemented in the organisation. Example • Wal-mart experienced internal changes in how they set their strategic objectives to how they train their employees to serve the customer, because of domestic and global geographic expansion, technology and information improvements and changing expectations of their customers In this case learning and organizational development helps by educating the organization on the importance of change management, identifying change management tools and skills needed for success and inculcating participation skills throughout the organization, where all stakeholders understand that HR is not solely responsibility to lead the change; rather, it is everyone’s responsibility. This results in building commitment; provides a pragmatic approach that institutionalizes positive and continuous change; involves all stakeholders in improving the organization’s overall performance. HR is increasingly taking the lead in helping organizations develop an understanding of the change process and how it relates to the business. It is also increasingly sought by upper management to help create and maintain company vision, courage, flexibility, patience, passion, values, prestige, and employee focus. Learning and development can happen in organisation by using either internal or outside resources to supplement training in the organisation. Learning and development in the organisation provides cross-cultural awareness, understanding and acceptance among the various employees of the organisation. It promotes awareness, understanding and acceptance of other cultures. For example Motorola sends its managers to a two day course on cross cultural communication

Compensation Organizations can not effectively review and model their compensation without integrating it with the HR practices/ strategies and goals of the organization. Also the global organizations try reinforcing strong personal commitment through reward systems that in alignment to the HR practices The rewards has to be in conjunction with the goals of the organisation. Compensation enhances the focus on organizational business unit goals and results; indexes total compensation costs with company performance; attracts entrepreneurial employees who thrive in performance-based environments. Through compensation organisation hope to attract, retain and motivate its employees. It is an important motivator and can enhance the productivity if employed properly. It includes gain sharing, team-based incentives, lump-sum bonuses, and profit sharing, spot awards ESOPs and other equitybased incentive awards. This helps to instill a sense of ownership in employees and results in alignment of employee and shareholder interests by providing incentives which focus on long-term, continuous improvement and company financial performance; links employees interests with financial performance of the company; reduces service operating costs and promote teamwork. It can also be used to minimize the employee dissatisfaction. Compensation includes • • •

Setting and managing salary and wage rates; Setting and managing, as well as other compensation elements such as incentive or variable pay programs; and Maintaining both internal and external equity, through job evaluation and salary surveys.

Global organizations also compensate employees for attaining skills that add value to the organization and or workforce flexibility. This improves compensation ROI by directing funds to individuals with competencies / skills which have the greatest impact on the organization’s performance / success; facilitates job-rotation, cross-training and self-managed work teams. Example General Mills rewards its employees for acquiring new skills. Compensation helps the organization to recognize exceptional performance and significant contributions toward key organizational goals with ad-hoc one-time rewards. This reinforces exceptional individual / team contributions;

CONCLUSION Globalization brings in significant changes not only in the operating boundaries but also in the corporate HR function and HR strategies. Organizations can develop competency models to identify critical success factors that differentiate high or low performers and that integrate HR systems (including selection, training & education, succession planning, career development, performance management and compensation). This will help the organization to links performance with key organizational objectives; links functional HR areas around a core set of competencies; develops an unambiguous profile of successful employees. Linking competency models to structured interview guides, compensation program design, training needs, curriculum and performance review can help organizations understand critical success factors and ensure smooth functioning. This may include the use of multi-rater feedback mechanisms, implementation of review process, which include self, peer and upward appraisals (in other words, 360-degree performance mechanism) and increase in the acceptance of feedback, which is received from more than one source In addition, to these changes the corporate HR function faces the complex issues associated with how to design flexible global HR strategies HR strategies can play more influential roles in global organizations than it has in the past With more and more organizations going global the organizations are trying to bridge the gap between their policies and trying to accommodate all employees from all nations. References 1. Abbas. J. Ali and Ahmed Azim; A cross-national perspective on managerial problems in a non-western country; The journal of social psychology;1996 2. Hodgetts & Luthans; International Management; Tata McGraw hill; 2003 3. Margaret Butteriss; Re-inventing HR; John Wiley & sons; 1998 4. www.thecommonwealth.org 5. www.igda.org

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IPR AND ITS IMPACT ON INDIAN ECONOMY Vinita Jagdev

In the past-GATT era, when India a signatory to the TRIPS and WTO being in its existence, IPR are being considered as tools to create wealth through knowledge. Now, there is a sea change in the economical and technological environment in the post-GATT world. TRIPS agreement, on one hand puts restrictions on dual use of technologies, marketing territorial restrictions and non-tariff barriers, on the other hand, have thrown challenges and opportunities for scientists and industrialists1. The major challenge is in the area of IPR, which has led to the recognition of importance of IPR by the R&D and industrial organization. Intellectual Property Rights as it relates to the commercial and industrial activities so may also be called as Industrial Property Rights, further, it is concerned with the intangible property so may also be known as Intangible Property Rights. Still further, one may call it Investment Protection and Rights, as IPR mainly concerned with monopoly/exclusive protection and rights for their investment. Intellectual property is intangible unlike movable property, such as a car and immovable property such as a house. It is creation of human intellect. An example is music. The distinctive feature of intellectual property is that it “relates to information which can be incorporated in tangible objects and reproduced in different locations and can be used by several persons at the same time unlike immovable or movable tangible property. The agreement of Trade Related Intellectual Property Rights (TRIPs) sets out the minimum standards of protection to be adopted by the parties in respect of: (i) Copyrights and related Rights (ii) Trade Marks, (iii) Geographical Indicators, (iv) Industrial Designs, (v) Patents, (vi) Layout Designs of Integrated Circuits, and (vii) Protection of undisclosed information (trade secrets) and the enforcement of these.

Whether Patent Required? In the modern world, new and improved technologies are being developed at a very fast rate than ever before. Here some may raise the question that when the technology is said to be ever changing/improving, then why do we need to go for safeguarding the IPRs. This is mainly due to desire of the inventor to have exclusive rights/ monopoly over the advancements made in technology and at the same time to exclude others from exploiting the same for commercial benefits. The award of exclusive rights/monopoly to the original inventor and penalty to the infringes of such rights are the basis for creation of IPR related laws. On the other hand, proper law enforcement of IPRs ensures better returns on inputs of the R&D efforts. It is observed that the development of a new technology is often followed by the challenge to utilize it or to transfer it for commercial exploitation. The utilization or transfer of technology is faced by another challenge, i.e., how to avoid unauthorized copying and are so that the hard inputs, e.g., intellectual and financial, are not wasted without appropriate returns. The only means to meet the challenge of avoiding the unauthorized copying or use of the technology is to safeguard the technology by IPR instruments. The appropriate return come only if the invention is kept secret by the means of trade secret or is safeguard by securing IPRs. If the invention is kept secret by means of trade secret, there is every chance of disclosure of information to the third party. Once the information is disclosed, then one cannot expect the return of his/her inputs. However, if the invention is safeguarded by securing the IPRs, then the risk due to disclosure is totally eliminated because the information is published by the government authorities itself in the form of patent documents and in return authorities grant the exclusive rights. The protection of technology from piracy and counterfeiting is increasingly becoming important for industrial investment, specially in technology sensitive sectors or where the technology is R&D intensive, such as

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information technology, defence sectors etc. This becomes more important because the investment required in bringing research activities to the industrial applications and/or market stage has already become very high. In the presence of IPR, the protection of intellectual properties, which particularly means the protection of knowledge, research and development for industrial investments, becomes possible due to the reasons explained earlier. The new technological information disclosed in the patent documents plays a vital role in the technological development. Therefore, such disclosure of inventions, in return of grant of exclusive rights by one may help others in the development of new technologies by way of providing solution to the ongoing technical problems. IPR and Indian Economy India is currently continuing her efforts towards globalisation and liberalisation of trade. The consequent readjustments in the economic, industrial, legal and R&D policies are generating a wide range of concerns and speculations. The issues relating to biodiversity, genetic engineering, environmental safety, agriculture and food security have been widely debated and yet, many aspects in these areas remain unclear and underestimated. These issues are yet to be fully understood and therefore the process of policy response has to rely on case studies, public debates and impact assessments The role of knowledge as potential contributor to production is increasingly being recognized.Not only gathering and generation of information and technology, but its effective protection also is important in the new order of international relations and multilateral trade. Traditional knowledge, ancient wisdom and even folk fore technologies are now viewed as a potential contributor to technology generation. However, it is axiomatic to say that IPRs play an important role in national economies today. Industrial advancement is to a great extend depends on IPRs. Even India is moving from brick and mortar economy to knowledge economy. The wheels of this new economy are intellectual property rights.With this aspect in view, in the following section, an attempt is made to understand the impact of IPRs on various vital sectors in India. Agriculture Sector IPRs and Agreement on Agriculture (AoA) were the two most controversial issues while establishing WTO. However, there are different views regarding the impact of patent regime on agriculture and there is no consensus on it. In the country, in order to fulfil the obligations under the TRIPS agreement of the WTO, the Parliament passed the protection of Plant Varieties and Farmers’ Rights Legislation in August 20015. The objective of this legislation is to provide an effective system for the protection of farmers’ rights which will also stimulate investment for research and development both in public and private sector for development of new plant varieties by ensuring appropriate returns on such investments. TRIPS offers three options as far as protection of new plant varieties is concerned: protection will have to be granted by a patent, an effective sui generis system or a combination of the two. India ultimately opted for the sui generis system after a determined struggle by civil society to stop seed patents. Obviously, the Multinational Corporations (MNCs) were interested in seed patents, as that could have guaranteed the seed market to them. In many developed countries, seed production is now in the hands of MNCs who have bought up all the smaller seed companies. However, in India, this strategy cannot work, as there are no seed companies of any significant size that can be bought. In fact, it is the farmers themselves who are the largest seed producers with 87 per cent stake6. So, if MNCs have to control seed production, they must knock out the farmers from the market. By opting for the sui generis system, the government has effectively blocked this strategy of the MNCs. On the other hand, the concept of diversity of biological organisms are a crucial component in the livelihood of many of the poor people of the developing countries as majority of them depend on the diversified plant and animals to meet nutritional and energy needs. Introduction of IPRs in agriculture may lead to erosion of biological diversity of cultivated plant spices as more and more area would be occupied by genetically uniform crops which will narrow the base of cultivated crops. In this way, the implication of IPRs on the issue of biodiversity of agriculture is doubtful.

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Further, the problem of biopiracy is very serious aspect for the developing countries like India. Haldi and Neem has become the symbols of piracy in India. India’s ancient use of Haldi was sought to be patented under the American Law in 1995. Luckily for India, Dr. R.A. Moshelkar, Director General of Council of Scientific and Industrial challenged it. The US Patent office acknowledged its mistake and cancelled the patent on ‘Haldi’. Similarly, an American Company has been granted a patent right for Neem as a pesticide. Basmati rice, which was a universal variety in India, has been patented as Kasmati and Texmati. No danger lurks with regard to Tulsi plant. These are a few cases of biopiracy of India’s herbal wealth and to prevent huge losses, India will have to undertake huge documentation about the use of its herbal wealth7.

Industrial Sector Amid so many changes around us, the Indian industrial sector more particularly small scale industries (SSIs) which has been playing important role in terms of its contribution towards employment, output and exports, has remained relatively oblivious to these changes. So far, small sector has survived amid somewhat protected environment in the form of product reservation, market reservation, price preference, priority sector tending, fiscal exemption/concession, etc. The emergence of patent and liberalized regime which consider protection as discrimination or barrier to trade, many of existing support systems in place for protection and promotion of SSIs will have to be dismantled. SSIs will have to compete on their own, to find a place for themselves in domestic as well as international market. It will have to adopt modern marketing, management practices and improvement in quality of its product and be efficient and competitive. Under 1994 TRIPS agreement, member states of WTO are required to promote effective and adequate protection of intellectual property rights with a view to reducing distortions and impediments to international trade. TRIPS agreement essentially mandates the protection of intellectual property, which is increasingly becoming an integral part of technology transfer and licence agreements in the context of liberalised economy. FDI agreements are also increasingly incorporating royalty payment clauses relating to the use of patents and trade marks. This becomes more significant for small and medium enterprises, which have to readjust to globalised economy and also to establish their competitiveness. Considerable controversy has been generated in the case of pharmaceuticals and agro-chemical sectors. In the developing country like India, existing laws are required to be amended to bring them in conformity with TRIPS. At present, there are no specific laws on geographical indication and trade secrets though action can be taken under common law. In this way, biggest challenge before Indian industry is to radically change its mindset. While agreement on TRIPS may have little direct implication for the small and medium enterprises, but those engaged in high-tech industries, such as electronics, pharmaceuticals, machine tools, biotechnology, etc. may face the problem of accessing appropriate technology under the TRIPS regime. It is apprehended that both terms and conditions and the cost of technology may be prohibitive. Main source of technology for SSI-reserve engineering will be difficult with stricter IPR regime and in the new regime ignorance of law will be of no excuse as the burden of proof is on infringer. While transfer of technology cases may increase, any counterfeit trade will have to take effective deterrent action. Care will have to be exercised in choosing the names of the companies or products. Problems may come before those SSIs who use protected designs as in the case of garment industries. Employees, sub-contractors etc. might have to be restrained from divulging confidential information. Till now, Indian industry, more particularly SSIs, has been limited to copying low end products and selling them in rural or low-end markets. But after TRIPS, the Indian industry will have to innovate and develop new products. Even in the sectors like garments, diversification may be answer to many troubles. Indian exports mainly low value added, non-branded cotton ready-made. With world renowned Indian designers, India can look forward to exporting high value added branded ready-mades in different categories.

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Pharmaceutical Industry Patent regime, the critics are of view, will affect the drug prices seriously. Currently, these prices are very low in India, thanks to the Indian Patent Act, 1970. Since the enforcement of this Act, Indian pharmaceutical and drug industry progressed rapidly and was able to provide life saving drugs at very cheap rates. However, under the new patent regime, as per the National Working Group on Patent Laws, about 70 per cent of drugs will be covered under the new patent laws. Consequently, under TRIPS, heavy payments will have to be made to patent holders and due to it, it is feared that this may result in the prices of drugs going up 5 to 10 times. At present, only 30 per cent of the population can afford modern drugs and after implementation of patent regime, only 10 per cent of the population may have access to modern drugs. With the adoption of TRIPS-Plus the monopoly rights of the transnational drug companies have been reinforced, making the development of such life-saving generics increasingly problematic and ensuring, at the very least, that the price of such drugs will rise.

Conclusion Although we are already on the road to globalization and IPR agreement in a big way after signing the WTO agreement and the process is irreversible and imminent, the journey is not smooth by any means. There are lots of contentious issues that still need to be addressed and many areas where India and other developing nations are at disadvantage10. There is need to use extensively, the patented and patentable inventions in order to make agriculture and small-scale industries viable in the global world. At the same time, the rural economy can also create patentable inventions, particularly those requiring low economic resources11

Message to the Sponsors The Department of Humanities & Applied Sciences the Institute of Technology and Management thanks the sponsors who came forward and helped us. We hope that like this year; in the years to come you shall continue to encourage us to work with the same enthusiasm. Thank you for your support!

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ancient india's contribution to mathematics

ANCIENT INDIA’S CONTRIBUTION TO MATHEMATICS A.P. Gupta
“India was the motherland of our race and Sanskrit the mother of Europe’s languages. India was...